(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 72996, 1926] NotebookOptionsPosition[ 67600, 1760] NotebookOutlinePosition[ 67980, 1776] CellTagsIndexPosition[ 67937, 1773] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"SetDirectory", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{ 3.6354940287861185`*^9, 3.635494073534405*^9, {3.6354941121292562`*^9, 3.6354941152387953`*^9}, 3.6354974933777275`*^9, 3.6659828997287407`*^9, { 3.6660061986053753`*^9, 3.6660062185118065`*^9}, {3.666327481132902*^9, 3.6663274833729053`*^9}, {3.666507623165536*^9, 3.666507624931184*^9}, 3.667216880725457*^9, {3.6689310468092213`*^9, 3.6689310483692236`*^9}, { 3.669529150401106*^9, 3.6695291524010935`*^9}, {3.6695332057232366`*^9, 3.669533209683242*^9}, 3.728818994303891*^9}], Cell[BoxData["\<\"C:\\\\Users\\\\Marica\\\\Dropbox\\\\Kagrujevac\\\\\ Mathematica\"\>"], "Output", CellChangeTimes->{3.7291947635408683`*^9, 3.7291948508235483`*^9}] }, Open ]], Cell[BoxData[ RowBox[{"<<", "Eigenvalues.m"}]], "Input", CellChangeTimes->{{3.6672168170840826`*^9, 3.667216823787284*^9}, { 3.7288190010378246`*^9, 3.7288190101440506`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", "Esercizio"}]}]}]}]}]}]}]}]}]}], " ", "1"}]], "Input", CellChangeTimes->{{3.729194107066983*^9, 3.7291941122277126`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"A", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", "6", ",", "10", ",", "12"}], "}"}], ",", RowBox[{"{", RowBox[{"7", ",", "8", ",", "14", ",", "16"}], "}"}], ",", RowBox[{"{", RowBox[{"15", ",", "18", ",", "20", ",", "24"}], "}"}], ",", RowBox[{"{", RowBox[{"21", ",", "24", ",", "28", ",", "32"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "MatrixForm"}], "\n", RowBox[{ RowBox[{"n", "=", "4"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"itmax", "=", "200"}], ";", RowBox[{"toll", "=", RowBox[{"2", " ", "$MachineEpsilon"}]}], ";"}], " "}]}], "Input", CellChangeTimes->{{3.729193528532745*^9, 3.7291935317764006`*^9}, 3.7291936350049996`*^9, {3.7291937596296434`*^9, 3.72919376104543*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"5", "6", "10", "12"}, {"7", "8", "14", "16"}, {"15", "18", "20", "24"}, {"21", "24", "28", "32"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.729194769958954*^9, 3.7291948564846106`*^9, 3.729254549898928*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", "Approximation"}]}]}], " ", "of", " ", "the", " ", "subdominant", " ", "eigenpair", " ", "by", " ", "HouseHolder", " ", "Deflation"}]], "Input", CellChangeTimes->{{3.7288324870522375`*^9, 3.728832494937882*^9}, { 3.7288325876445293`*^9, 3.728832611463897*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"PowerMethod", "[", RowBox[{"A", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.728819337043078*^9, 3.7288193428324795`*^9}, { 3.7288195724195585`*^9, 3.7288195769907*^9}, {3.728822542373357*^9, 3.72882254908121*^9}, {3.728824208554889*^9, 3.7288242358375196`*^9}, { 3.72893241810643*^9, 3.7289324216227674`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"70.65660577509668`", ",", RowBox[{"{", RowBox[{ "0.3366707522687819`", ",", "0.45742710775633816`", ",", "0.7360096211178622`", ",", "1.`"}], "}"}], ",", "15"}], "}"}]], "Output", CellChangeTimes->{3.729254587569457*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{"70.65660577509668`", ",", RowBox[{"{", RowBox[{ "0.3366707522687819`", ",", "0.45742710775633816`", ",", "0.7360096211178622`", ",", "1.`"}], "}"}], ",", "15"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7291948732532187`*^9, 3.7291948732773085`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"A2", "=", RowBox[{"HouseHolderDeflatedMatrix", "[", RowBox[{"A", ",", "t"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "MatrixForm"}]}], "Input", CellChangeTimes->{{3.7288318659339895`*^9, 3.728831901249915*^9}, { 3.7289324271023517`*^9, 3.7289324386611214`*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"-", "1.6287287982237553`"}], "1.677750302130777`", "1.7108453031868658`"}, {"1.5029026262718377`", RowBox[{"-", "1.4426518631331995`"}], RowBox[{"-", "1.1870296033814212`"}]}, {"1.41917965628519`", RowBox[{"-", "1.401685846229424`"}], RowBox[{"-", "2.585225113739721`"}]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.729194865947794*^9, 3.729254704738126*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", RowBox[{"n", "-", "1"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"PowerMethod", "[", RowBox[{"A2", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.728819337043078*^9, 3.7288193428324795`*^9}, { 3.7288195724195585`*^9, 3.7288195769907*^9}, {3.728822542373357*^9, 3.72882254908121*^9}, {3.728824208554889*^9, 3.7288242358375196`*^9}, { 3.728832715859658*^9, 3.728832722271686*^9}, {3.7289324516837482`*^9, 3.728932454872249*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "4.896269035971499`"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "0.901499431700626`"}], ",", "0.7360096211178628`", ",", "1.`"}], "}"}], ",", "23"}], "}"}]], "Output", CellChangeTimes->{3.7292547256391487`*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "4.896269035971498`"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "0.9014994317006259`"}], ",", "0.7360096211178626`", ",", "0.9999999999999999`"}], "}"}], ",", "22"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.729194877939687*^9, 3.729194877963751*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"InversePowerMethodImprove", "[", RowBox[{"A", ",", "lam", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.728828274199732*^9, 3.7288282854884624`*^9}, { 3.7288340958318524`*^9, 3.7288340970631585`*^9}, {3.728834168134203*^9, 3.7288341711121254`*^9}, 3.7288342073183403`*^9, {3.7288343446833487`*^9, 3.7288343461061583`*^9}, 3.728834444008589*^9, {3.7288347329001446`*^9, 3.728834733057583*^9}, {3.7289324617354803`*^9, 3.728932465975763*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LUDecomposition", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LUDecomposition\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({9.8962690359715`, 6.`, 10.`, \ 12.`}\\)\\), \\(\\({7.`, 12.8962690359715`, 14.`, 16.`}\\)\\), \\(\\({15.`, \ 18.`, \\(\\(\[LeftSkeleton] 17 \[RightSkeleton]\\)\\), 24.`}\\)\\), \ \\(\\({21.`, 24.`, 28.`, 36.8962690359715`}\\)\\)}\\)\[NoBreak] may contain \ significant numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LUDecomposition::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.729194881351774*^9, 3.729254850307146*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\(\[LeftSkeleton] 1 \ \[RightSkeleton]\\)\[NoBreak] may contain significant numerical errors. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/General/luc\\\", \ ButtonNote -> \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.729194881351774*^9, 3.7292548503402023`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\(\[LeftSkeleton] 1 \ \[RightSkeleton]\\)\[NoBreak] may contain significant numerical errors. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/General/luc\\\", \ ButtonNote -> \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.729194881351774*^9, 3.7292548503712854`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "4.896269035971499`"}], ",", RowBox[{"{", RowBox[{"0.7360096211178623`", ",", "1.`", ",", RowBox[{"-", "0.5050061284031728`"}], ",", RowBox[{"-", "0.6861406616345072`"}]}], "}"}], ",", "3"}], "}"}]], "Output", CellChangeTimes->{3.7292548503723245`*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "4.8962690359715`"}], ",", RowBox[{"{", RowBox[{"0.7360096211178621`", ",", "1.`", ",", RowBox[{"-", "0.5050061284031728`"}], ",", RowBox[{"-", "0.6861406616345072`"}]}], "}"}], ",", "3"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.729194884430956*^9, 3.7291948844580283`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", "Approximation"}]}]}], " ", "of", " ", "the", " ", "next", " ", "least", " ", "dominant", " ", "eigenpair", " ", "by", " ", "HouseHolder", " ", "Deflation"}]], "Input", CellChangeTimes->{{3.7288327843009777`*^9, 3.7288328207636557`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"InversePowerMethod", "[", RowBox[{"A", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.7288241902161283`*^9, 3.7288242031846294`*^9}, { 3.728824239105164*^9, 3.728824240024612*^9}, 3.7288256800643606`*^9, { 3.728827747279608*^9, 3.7288277481619277`*^9}, 3.7288277953635*^9, { 3.728828162713482*^9, 3.728828182935279*^9}, 3.7288282323430004`*^9, { 3.72892393428718*^9, 3.7289239384803104`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"0.05661183347431365`", ",", RowBox[{"{", RowBox[{"1.`", ",", RowBox[{"-", "0.8586778913041725`"}], ",", RowBox[{"-", "0.6861406616345072`"}], ",", "0.5891738164703685`"}], "}"}], ",", "17"}], "}"}]], "Output", CellChangeTimes->{3.729254898412983*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{"0.05661183347431365`", ",", RowBox[{"{", RowBox[{"1.`", ",", RowBox[{"-", "0.8586778913041725`"}], ",", RowBox[{"-", "0.6861406616345072`"}], ",", "0.5891738164703685`"}], "}"}], ",", "18"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.729194894449609*^9, 3.7291948944716682`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"A2", "=", RowBox[{"HouseHolderDeflatedMatrix", "[", RowBox[{"A", ",", "t"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "MatrixForm"}]}], "Input", CellChangeTimes->{{3.7288318659339895`*^9, 3.728831901249915*^9}, { 3.728932475280542*^9, 3.728932485252043*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"13.105141935437288`", "19.803103052655942`", "18.087306844318686`"}, {"25.187734822280923`", "27.120872679956`", "23.535105821763455`"}, {"29.023744892605226`", "30.831566995483655`", "24.717373551132397`"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.729194897245077*^9, 3.7292549129376383`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", RowBox[{"n", "-", "1"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"InversePowerMethod", "[", RowBox[{"A2", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.7288241902161283`*^9, 3.7288242031846294`*^9}, { 3.728824239105164*^9, 3.728824240024612*^9}, 3.7288256800643606`*^9, { 3.728827747279608*^9, 3.7288277481619277`*^9}, 3.7288277953635*^9, { 3.728828162713482*^9, 3.728828182935279*^9}, 3.7288282323430004`*^9, { 3.7288328829500666`*^9, 3.728832886869494*^9}, {3.7289324958522425`*^9, 3.7289325009608617`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "0.8169485725994892`"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "0.30684562420699696`"}], ",", "1.`", ",", RowBox[{"-", "0.8586778913041722`"}]}], "}"}], ",", "23"}], "}"}]], "Output", CellChangeTimes->{3.7292549187433147`*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "0.8169485725994893`"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "0.306845624206997`"}], ",", "1.`", ",", RowBox[{"-", "0.858677891304172`"}]}], "}"}], ",", "22"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7291949027105856`*^9, 3.7291949027336483`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"InversePowerMethodImprove", "[", RowBox[{"A", ",", "lam", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.728828274199732*^9, 3.7288282854884624`*^9}, { 3.7288340958318524`*^9, 3.7288340970631585`*^9}, {3.728834168134203*^9, 3.7288341711121254`*^9}, 3.7288342073183403`*^9, {3.7288343446833487`*^9, 3.7288343461061583`*^9}, 3.728834444008589*^9, {3.7288347329001446`*^9, 3.728834733057583*^9}, {3.7289325067783103`*^9, 3.7289325124744916`*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LUDecomposition", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LUDecomposition\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({5.81694857259949`, 6.`, \ 10.`, 12.`}\\)\\), \\(\\({7.`, 8.81694857259949`, 14.`, 16.`}\\)\\), \ \\(\\({15.`, \\(\\(\[LeftSkeleton] 2 \[RightSkeleton]\\)\\), 24.`}\\)\\), \\(\ \\({21.`, 24.`, 28.`, 32.816948572599486`}\\)\\)}\\)\[NoBreak] may contain \ significant numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LUDecomposition::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.7291949062530107`*^9, 3.7292549295468826`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({21.`, 24.`, 28.`, \ 32.816948572599486`}\\)\\), \\(\\({0.`, \\(\\(\[LeftSkeleton] 19 \ \[RightSkeleton]\\)\\), \\(\\(\[LeftSkeleton] 19 \[RightSkeleton]\\)\\), \ 0.5593224481432273`}\\)\\), \\(\\({\\(\[LeftSkeleton] 1 \ \[RightSkeleton]\\)}\\)\\), \\(\\({0.`, 0.`, 0.`, 8.881784197001252`*^-15}\\)\ \\)}\\)\[NoBreak] may contain significant numerical errors. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/General/luc\\\", \ ButtonNote -> \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.7291949062530107`*^9, 3.729254929577963*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({21.`, 24.`, 28.`, \ 32.816948572599486`}\\)\\), \\(\\({0.`, \\(\\(\[LeftSkeleton] 19 \ \[RightSkeleton]\\)\\), \\(\\(\[LeftSkeleton] 19 \[RightSkeleton]\\)\\), \ 0.5593224481432273`}\\)\\), \\(\\({\\(\[LeftSkeleton] 1 \ \[RightSkeleton]\\)}\\)\\), \\(\\({0.`, 0.`, 0.`, 8.881784197001252`*^-15}\\)\ \\)}\\)\[NoBreak] may contain significant numerical errors. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/General/luc\\\", \ ButtonNote -> \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.7291949062530107`*^9, 3.7292549296080723`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({21.`, 24.`, 28.`, \ 32.816948572599486`}\\)\\), \\(\\({0.`, \\(\\(\[LeftSkeleton] 19 \ \[RightSkeleton]\\)\\), \\(\\(\[LeftSkeleton] 19 \[RightSkeleton]\\)\\), \ 0.5593224481432273`}\\)\\), \\(\\({\\(\[LeftSkeleton] 1 \ \[RightSkeleton]\\)}\\)\\), \\(\\({0.`, 0.`, 0.`, 8.881784197001252`*^-15}\\)\ \\)}\\)\[NoBreak] may contain significant numerical errors. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/General/luc\\\", \ ButtonNote -> \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.7291949062530107`*^9, 3.7292549296366725`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"General", "::", "stop"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Further output of \ \[NoBreak]\\!\\(\\*StyleBox[\\(LinearSolve :: luc\\), \\\"MessageName\\\"]\\)\ \[NoBreak] will be suppressed during this calculation. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/General/stop\\\", \ ButtonNote -> \\\"General::stop\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.7291949062530107`*^9, 3.7292549296527414`*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "0.8169485725994916`"}], ",", RowBox[{"{", RowBox[{"0.45742710775633777`", ",", RowBox[{"-", "0.39278254431357873`"}], ",", "1.`", ",", RowBox[{"-", "0.8586778913041725`"}]}], "}"}], ",", "4"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.729254934429095*^9, 3.7292549344461684`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "0.8169485725994917`"}], ",", RowBox[{"{", RowBox[{"0.45742710775633777`", ",", RowBox[{"-", "0.39278254431357873`"}], ",", "1.`", ",", RowBox[{"-", "0.8586778913041725`"}]}], "}"}], ",", "4"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7291949098977065`*^9, 3.7291949099257817`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"-", "Esercizio"}]}]}]}]}]}]}]}]}]}]}], " ", "2"}]], "Input", CellChangeTimes->{{3.7291940961048203`*^9, 3.729194101098135*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"A", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"4", ",", "3", ",", "2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "4", ",", "3", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "3", ",", "4", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}]}], "}"}]}], ";"}], "\n", RowBox[{"%", "//", "MatrixForm"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"n", "=", "4"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"itmax", "=", "200"}], ";", RowBox[{"toll", "=", RowBox[{"2", " ", "$MachineEpsilon"}]}], ";"}], " "}]}], "Input", CellChangeTimes->{{3.7288192178763666`*^9, 3.7288192973574996`*^9}, { 3.7291939868100567`*^9, 3.7291940141748567`*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"4", "3", "2", "1"}, {"3", "4", "3", "2"}, {"2", "3", "4", "3"}, {"1", "2", "3", "4"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.7291946376831827`*^9, 3.7291947742824454`*^9, 3.729194912711192*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", "Approximation"}]}]}], " ", "of", " ", "the", " ", "subdominant", " ", "eigenpair", " ", "by", " ", "HouseHolder", " ", "Deflation"}]], "Input", CellChangeTimes->{{3.7288324870522375`*^9, 3.728832494937882*^9}, { 3.7288325876445293`*^9, 3.728832611463897*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"PowerMethod", "[", RowBox[{"A", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.728819337043078*^9, 3.7288193428324795`*^9}, { 3.7288195724195585`*^9, 3.7288195769907*^9}, {3.728822542373357*^9, 3.72882254908121*^9}, {3.728824208554889*^9, 3.7288242358375196`*^9}, { 3.72893241810643*^9, 3.7289324216227674`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"11.099019513592784`", ",", RowBox[{"{", RowBox[{ "0.819803902718557`", ",", "1.`", ",", "1.`", ",", "0.819803902718557`"}], "}"}], ",", "32"}], "}"}]], "Output", CellChangeTimes->{3.7291946452703657`*^9, 3.729194919783839*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{"11.099019513592783`", ",", RowBox[{"{", RowBox[{ "0.8198039027185569`", ",", "1.0000000000000002`", ",", "1.`", ",", "0.8198039027185571`"}], "}"}], ",", "31"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7289326050337067`*^9, 3.7289326050517545`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"A2", "=", RowBox[{"HouseHolderDeflatedMatrix", "[", RowBox[{"A", ",", "t"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "MatrixForm"}]}], "Input", CellChangeTimes->{{3.7288318659339895`*^9, 3.728831901249915*^9}, { 3.7289324271023517`*^9, 3.7289324386611214`*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0.7225371781422766`", "0.10010831841197443`", RowBox[{"-", "0.1358450696026522`"}]}, {"0.10010831841197476`", "1.4776794586816726`", "1.1736892247443422`"}, { RowBox[{"-", "0.13584506960265186`"}], "1.1736892247443422`", "2.7007638495832653`"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.7289326089571447`*^9, 3.7291946501744113`*^9, 3.7291949230374928`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", RowBox[{"n", "-", "1"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"PowerMethod", "[", RowBox[{"A2", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.728819337043078*^9, 3.7288193428324795`*^9}, { 3.7288195724195585`*^9, 3.7288195769907*^9}, {3.728822542373357*^9, 3.72882254908121*^9}, {3.728824208554889*^9, 3.7288242358375196`*^9}, { 3.728832715859658*^9, 3.728832722271686*^9}, {3.7289324516837482`*^9, 3.728932454872249*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"3.414213562373095`", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "0.027981261935312127`"}], ",", "0.6046307500771642`", ",", "1.`"}], "}"}], ",", "28"}], "}"}]], "Output", CellChangeTimes->{3.729194654026661*^9, 3.729194926085598*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{"3.4142135623730963`", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "0.0279812619353116`"}], ",", "0.6046307500771645`", ",", "1.`"}], "}"}], ",", "27"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7289326143895955`*^9, 3.7289326144096484`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"InversePowerMethodImprove", "[", RowBox[{"A", ",", "lam", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.728828274199732*^9, 3.7288282854884624`*^9}, { 3.7288340958318524`*^9, 3.7288340970631585`*^9}, {3.728834168134203*^9, 3.7288341711121254`*^9}, 3.7288342073183403`*^9, {3.7288343446833487`*^9, 3.7288343461061583`*^9}, 3.728834444008589*^9, {3.7288347329001446`*^9, 3.728834733057583*^9}, {3.7289324617354803`*^9, 3.728932465975763*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LUDecomposition", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LUDecomposition\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({0.5857864376269051`, 3.`, \ 2.`, 1.`}\\)\\), \\(\\({3.`, 0.5857864376269051`, 3.`, 2.`}\\)\\), \ \\(\\({2.`, 3.`, 0.5857864376269051`, 3.`}\\)\\), \\(\\({1.`, 2.`, 3.`, \ 0.5857864376269051`}\\)\\)}\\)\[NoBreak] may contain significant numerical \ errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LUDecomposition::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.728834769108473*^9, 3.7289223212362657`*^9, 3.728932625406906*^9, 3.7291946581536407`*^9, 3.7291949294455376`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({3.`, 0.5857864376269051`, \ 3.`, 2.`}\\)\\), \\(\\({0.`, 2.8856180831641267`, 1.414213562373095`, \ 0.60947570824873`}\\)\\), \\(\\({0.`, 0.`, \\(\\(-2.6930924129110556`\\)\\), \ 1.1155154021518427`}\\)\\), \\(\\({0.`, 0.`, 0.`, \ 3.3306690738754696`*^-16}\\)\\)}\\)\[NoBreak] may contain significant \ numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.728834769108473*^9, 3.7289223212362657`*^9, 3.728932625406906*^9, 3.7291946581536407`*^9, 3.7291949294806314`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({3.`, 0.5857864376269051`, \ 3.`, 2.`}\\)\\), \\(\\({0.`, 2.8856180831641267`, 1.414213562373095`, \ 0.60947570824873`}\\)\\), \\(\\({0.`, 0.`, \\(\\(-2.6930924129110556`\\)\\), \ 1.1155154021518427`}\\)\\), \\(\\({0.`, 0.`, 0.`, \ 3.3306690738754696`*^-16}\\)\\)}\\)\[NoBreak] may contain significant \ numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.728834769108473*^9, 3.7289223212362657`*^9, 3.728932625406906*^9, 3.7291946581536407`*^9, 3.729194929515723*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"3.414213562373095`", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.`"}], ",", RowBox[{"-", "0.4142135623730949`"}], ",", "0.4142135623730949`", ",", "1.`"}], "}"}], ",", "3"}], "}"}]], "Output", CellChangeTimes->{3.7291946582719545`*^9, 3.729194929517729*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{"3.414213562373095`", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.`"}], ",", RowBox[{"-", "0.41421356237309503`"}], ",", "0.41421356237309503`", ",", "1.`"}], "}"}], ",", "4"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7289326308173*^9, 3.728932630838386*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", "Approximation"}]}]}], " ", "of", " ", "the", " ", "next", " ", "least", " ", "dominant", " ", "eigenpair", " ", "by", " ", "HouseHolder", " ", "Deflation"}]], "Input", CellChangeTimes->{{3.7288327843009777`*^9, 3.7288328207636557`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"InversePowerMethod", "[", RowBox[{"A", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.7288241902161283`*^9, 3.7288242031846294`*^9}, { 3.728824239105164*^9, 3.728824240024612*^9}, 3.7288256800643606`*^9, { 3.728827747279608*^9, 3.7288277481619277`*^9}, 3.7288277953635*^9, { 3.728828162713482*^9, 3.728828182935279*^9}, 3.7288282323430004`*^9, { 3.72892393428718*^9, 3.7289239384803104`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"0.5857864376269053`", ",", RowBox[{"{", RowBox[{"0.4142135623730929`", ",", RowBox[{"-", "0.9999999999999974`"}], ",", "0.9999999999999999`", ",", RowBox[{"-", "0.4142135623730961`"}]}], "}"}], ",", "88"}], "}"}]], "Output", CellChangeTimes->{3.729194663121868*^9, 3.7291949345641546`*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{"0.5857864376269046`", ",", RowBox[{"{", RowBox[{"0.4142135623730966`", ",", RowBox[{"-", "1.0000000000000022`"}], ",", "0.9999999999999999`", ",", RowBox[{"-", "0.4142135623730942`"}]}], "}"}], ",", "79"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.72893265030715*^9, 3.728932650327203*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"A2", "=", RowBox[{"HouseHolderDeflatedMatrix", "[", RowBox[{"A", ",", "t"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "MatrixForm"}]}], "Input", CellChangeTimes->{{3.7288318659339895`*^9, 3.728831901249915*^9}, { 3.728932475280542*^9, 3.728932485252043*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"7.9874742760511905`", "1.5832894772876507`", "3.526911548047949`"}, {"1.583289477287651`", "2.8459467693734952`", "2.5379336642421673`"}, {"3.5269115480479485`", "2.5379336642421673`", "4.580792516948408`"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.728932657799096*^9, 3.729194667257861*^9, 3.729194937582183*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", RowBox[{"n", "-", "1"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"InversePowerMethod", "[", RowBox[{"A2", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.7288241902161283`*^9, 3.7288242031846294`*^9}, { 3.728824239105164*^9, 3.728824240024612*^9}, 3.7288256800643606`*^9, { 3.728827747279608*^9, 3.7288277481619277`*^9}, 3.7288277953635*^9, { 3.728828162713482*^9, 3.728828182935279*^9}, 3.7288282323430004`*^9, { 3.7288328829500666`*^9, 3.728832886869494*^9}, {3.7289324958522425`*^9, 3.7289325009608617`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"0.9009804864072152`", ",", RowBox[{"{", RowBox[{"0.22913124746210925`", ",", "1.`", ",", RowBox[{"-", "0.9093016923592167`"}]}], "}"}], ",", "30"}], "}"}]], "Output", CellChangeTimes->{3.7291946703029604`*^9, 3.729194940516004*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{"0.900980486407215`", ",", RowBox[{"{", RowBox[{"0.22913124746210592`", ",", "1.`", ",", RowBox[{"-", "0.9093016923592151`"}]}], "}"}], ",", "30"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7289326703945885`*^9, 3.7289326704166493`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"InversePowerMethodImprove", "[", RowBox[{"A", ",", "lam", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.728828274199732*^9, 3.7288282854884624`*^9}, { 3.7288340958318524`*^9, 3.7288340970631585`*^9}, {3.728834168134203*^9, 3.7288341711121254`*^9}, 3.7288342073183403`*^9, {3.7288343446833487`*^9, 3.7288343461061583`*^9}, 3.728834444008589*^9, {3.7288347329001446`*^9, 3.728834733057583*^9}, {3.7289325067783103`*^9, 3.7289325124744916`*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LUDecomposition", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LUDecomposition\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({3.099019513592785`, 3.`, \ 2.`, 1.`}\\)\\), \\(\\({3.`, 3.099019513592785`, 3.`, 2.`}\\)\\), \\(\\({2.`, \ 3.`, 3.099019513592785`, 3.`}\\)\\), \\(\\({1.`, 2.`, 3.`, \ 3.099019513592785`}\\)\\)}\\)\[NoBreak] may contain significant numerical \ errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LUDecomposition::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.728834848558838*^9, 3.7289240667154617`*^9, 3.728932682687293*^9, 3.7291946729088945`*^9, 3.7291949449277244`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({3.099019513592785`, 3.`, \ 2.`, 1.`}\\)\\), \\(\\({0.`, 1.0639037690201496`, 1.8082886929395514`, \ 2.3546345896733833`}\\)\\), \\(\\({0.`, 0.`, 0.732679675728523`, \ 0.6006536576048098`}\\)\\), \\(\\({0.`, 0.`, 0.`, \ 1.6653345369377348`*^-16}\\)\\)}\\)\[NoBreak] may contain significant \ numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.728834848558838*^9, 3.7289240667154617`*^9, 3.728932682687293*^9, 3.7291946729088945`*^9, 3.7291949449618287`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({3.099019513592785`, 3.`, \ 2.`, 1.`}\\)\\), \\(\\({0.`, 1.0639037690201496`, 1.8082886929395514`, \ 2.3546345896733833`}\\)\\), \\(\\({0.`, 0.`, 0.732679675728523`, \ 0.6006536576048098`}\\)\\), \\(\\({0.`, 0.`, 0.`, \ 1.6653345369377348`*^-16}\\)\\)}\\)\[NoBreak] may contain significant \ numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.728834848558838*^9, 3.7289240667154617`*^9, 3.728932682687293*^9, 3.7291946729088945`*^9, 3.729194944991896*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({3.099019513592785`, 3.`, \ 2.`, 1.`}\\)\\), \\(\\({0.`, 1.0639037690201496`, 1.8082886929395514`, \ 2.3546345896733833`}\\)\\), \\(\\({0.`, 0.`, 0.732679675728523`, \ 0.6006536576048098`}\\)\\), \\(\\({0.`, 0.`, 0.`, \ 1.6653345369377348`*^-16}\\)\\)}\\)\[NoBreak] may contain significant \ numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.728834848558838*^9, 3.7289240667154617`*^9, 3.728932682687293*^9, 3.7291946729088945`*^9, 3.7291949450239816`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"General", "::", "stop"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Further output of \ \[NoBreak]\\!\\(\\*StyleBox[\\(LinearSolve :: luc\\), \\\"MessageName\\\"]\\)\ \[NoBreak] will be suppressed during this calculation. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/General/stop\\\", \ ButtonNote -> \\\"General::stop\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.728834848558838*^9, 3.7289240667154617`*^9, 3.728932682687293*^9, 3.7291946729088945`*^9, 3.7291949450410275`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"0.9009804864072152`", ",", RowBox[{"{", RowBox[{"1.`", ",", RowBox[{"-", "0.819803902718557`"}], ",", RowBox[{"-", "0.8198039027185569`"}], ",", "1.`"}], "}"}], ",", "4"}], "}"}]], "Output", CellChangeTimes->{3.7291946730242257`*^9, 3.729194945042055*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{"0.900980486407215`", ",", RowBox[{"{", RowBox[{"1.`", ",", RowBox[{"-", "0.819803902718557`"}], ",", RowBox[{"-", "0.8198039027185569`"}], ",", "1.`"}], "}"}], ",", "4"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7289326865806694`*^9, 3.7289326865997267`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", "Esercizio"}]}]}]}]}]}]}]}]}], " ", "3"}]], "Input", CellChangeTimes->{{3.728924150656789*^9, 3.7289241837377987`*^9}, { 3.729194120469639*^9, 3.7291941210170965`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"A", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"944", "/", "281"}], ",", RowBox[{"5664", "/", "263"}], ",", RowBox[{ RowBox[{"-", "4349"}], "/", "367"}], ",", RowBox[{ RowBox[{"-", "5920"}], "/", "119"}], ",", RowBox[{ RowBox[{"-", " ", "3196"}], "/", "661"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "1", ",", "0"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "MatrixForm"}]}], "Input", CellChangeTimes->{{3.7288192178763666`*^9, 3.7288192973574996`*^9}, { 3.7289312486616116`*^9, 3.7289314532749767`*^9}, {3.7289321661731777`*^9, 3.728932223254033*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { FractionBox["944", "281"], FractionBox["5664", "263"], RowBox[{"-", FractionBox["4349", "367"]}], RowBox[{"-", FractionBox["5920", "119"]}], RowBox[{"-", FractionBox["3196", "661"]}]}, {"1", "0", "0", "0", "0"}, {"0", "1", "0", "0", "0"}, {"0", "0", "1", "0", "0"}, {"0", "0", "0", "1", "0"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.7289327953710723`*^9}] }, Open ]], Cell[BoxData[{ RowBox[{ RowBox[{"n", "=", "5"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"itmax", "=", "200"}], ";", RowBox[{"toll", "=", RowBox[{"2", " ", "$MachineEpsilon"}]}], ";"}], " "}]}], "Input", CellChangeTimes->{{3.728819346357831*^9, 3.7288194902699924`*^9}, { 3.7288195561713395`*^9, 3.7288195662471457`*^9}, {3.728819632262392*^9, 3.7288196408659945`*^9}, {3.7288202055482817`*^9, 3.728820209228072*^9}, { 3.7288207977978535`*^9, 3.728820809477954*^9}, {3.728821579888439*^9, 3.7288216346782*^9}, {3.728822360750187*^9, 3.7288223674189215`*^9}, { 3.7288224070372944`*^9, 3.728822407524591*^9}, 3.7288242321867604`*^9, 3.7288245948977013`*^9, {3.728931523116761*^9, 3.7289315236772795`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", "Approximation"}]}]}], " ", "of", " ", "the", " ", "subdominant", " ", "eigenpair", " ", "by", " ", "HouseHolder", " ", "Deflation"}]], "Input", CellChangeTimes->{{3.7288324870522375`*^9, 3.728832494937882*^9}, { 3.7288325876445293`*^9, 3.728832611463897*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"PowerMethod", "[", RowBox[{"A", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.728819337043078*^9, 3.7288193428324795`*^9}, { 3.7288195724195585`*^9, 3.7288195769907*^9}, {3.728822542373357*^9, 3.72882254908121*^9}, {3.728824208554889*^9, 3.7288242358375196`*^9}, { 3.72893241810643*^9, 3.7289324216227674`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{"6.283185295796321`", ",", RowBox[{"{", RowBox[{ "1.`", ",", "0.1591549433802368`", ",", "0.025330296002366394`", ",", "0.004031441826061261`", ",", "0.0006416238955674991`"}], "}"}], ",", "55"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.728932804679842*^9, 3.7289328047039003`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"A2", "=", RowBox[{"HouseHolderDeflatedMatrix", "[", RowBox[{"A", ",", "t"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "MatrixForm"}]}], "Input", CellChangeTimes->{{3.7288318659339895`*^9, 3.728831901249915*^9}, { 3.7289324271023517`*^9, 3.7289324386611214`*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"-", "3.4222170899854634`"}], "1.8558682065486953`", "7.815732233371857`", "0.7595745459375366`"}, {"0.467921145701073`", "0.2973733912783611`", "1.2442311753158275`", "0.12094077516452846`"}, { RowBox[{"-", "0.08468297992976698`"}], "1.0473284452516964`", "0.19802554225931596`", "0.01924832222367247`"}, { RowBox[{"-", "0.013477714875991805`"}], "0.00753255602430841`", "1.0315167439661221`", "0.003063465633673149`"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.728932807446198*^9}] }, Open ]], Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", RowBox[{"n", "-", "1"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"PowerMethod", "[", RowBox[{"A2", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.728819337043078*^9, 3.7288193428324795`*^9}, { 3.7288195724195585`*^9, 3.7288195769907*^9}, {3.728822542373357*^9, 3.72882254908121*^9}, {3.728824208554889*^9, 3.7288242358375196`*^9}, { 3.728832715859658*^9, 3.728832722271686*^9}, {3.7289324516837482`*^9, 3.728932454872249*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "3.1415918306351887`"}], ",", RowBox[{"{", RowBox[{"0.9999999999999999`", ",", RowBox[{"-", "0.16306409940784408`"}], ",", "0.0766130761950312`", ",", RowBox[{"-", "0.02045428210777507`"}]}], "}"}], ",", "64"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.728932814932132*^9, 3.728932814953167*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"InversePowerMethodImprove", "[", RowBox[{"A", ",", "lam", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.728828274199732*^9, 3.7288282854884624`*^9}, { 3.7288340958318524`*^9, 3.7288340970631585`*^9}, {3.728834168134203*^9, 3.7288341711121254`*^9}, 3.7288342073183403`*^9, {3.7288343446833487`*^9, 3.7288343461061583`*^9}, 3.728834444008589*^9, {3.7288347329001446`*^9, 3.728834733057583*^9}, {3.7289324617354803`*^9, 3.728932465975763*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LUDecomposition", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LUDecomposition\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({6.501022435617395`, \ 21.5361216730038`, \\(\\(-11.850136239782016`\\)\\), \ \\(\\(-49.747899159663866`\\)\\), \\(\\(-4.835098335854766`\\)\\)}\\)\\), \\(\ \\({1.`, 3.1415918306351887`, 0.`, 0.`, 0.`}\\)\\), \\(\\({0.`, 1.`, \ 3.1415918306351887`, 0.`, 0.`}\\)\\), \\(\\({0.`, 0.`, 1.`, \ 3.1415918306351887`, 0.`}\\)\\), \\(\\({0.`, 0.`, 0.`, 1.`, \ 3.1415918306351887`}\\)\\)}\\)\[NoBreak] may contain significant numerical \ errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LUDecomposition::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.728932818799401*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({6.501022435617395`, \ 21.5361216730038`, \\(\\(-11.850136239782016`\\)\\), \ \\(\\(-49.747899159663866`\\)\\), \\(\\(-4.835098335854766`\\)\\)}\\)\\), \\(\ \\({0.`, 1.`, 3.1415918306351887`, 0.`, 0.`}\\)\\), \\(\\({0.`, 0.`, \\(\\(\ \[LeftSkeleton] 19 \[RightSkeleton]\\)\\), 7.652319254754174`, \ 0.7437442931075782`}\\)\\), \\(\\({0.`, 0.`, 0.`, 1.`, \ 3.1415918306351887`}\\)\\), \\(\\({0.`, 0.`, 0.`, 0.`, \ \\(\\(-1.7263968032921184`*^-14\\)\\)}\\)\\)}\\)\[NoBreak] may contain \ significant numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.7289328188334923`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({6.501022435617395`, \ 21.5361216730038`, \\(\\(-11.850136239782016`\\)\\), \ \\(\\(-49.747899159663866`\\)\\), \\(\\(-4.835098335854766`\\)\\)}\\)\\), \\(\ \\({0.`, 1.`, 3.1415918306351887`, 0.`, 0.`}\\)\\), \\(\\({0.`, 0.`, \\(\\(\ \[LeftSkeleton] 19 \[RightSkeleton]\\)\\), 7.652319254754174`, \ 0.7437442931075782`}\\)\\), \\(\\({0.`, 0.`, 0.`, 1.`, \ 3.1415918306351887`}\\)\\), \\(\\({0.`, 0.`, 0.`, 0.`, \ \\(\\(-1.7263968032921184`*^-14\\)\\)}\\)\\)}\\)\[NoBreak] may contain \ significant numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.7289328188625984`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({6.501022435617395`, \ 21.5361216730038`, \\(\\(-11.850136239782016`\\)\\), \ \\(\\(-49.747899159663866`\\)\\), \\(\\(-4.835098335854766`\\)\\)}\\)\\), \\(\ \\({0.`, 1.`, 3.1415918306351887`, 0.`, 0.`}\\)\\), \\(\\({0.`, 0.`, \\(\\(\ \[LeftSkeleton] 19 \[RightSkeleton]\\)\\), 7.652319254754174`, \ 0.7437442931075782`}\\)\\), \\(\\({0.`, 0.`, 0.`, 1.`, \ 3.1415918306351887`}\\)\\), \\(\\({0.`, 0.`, 0.`, 0.`, \ \\(\\(-1.7263968032921184`*^-14\\)\\)}\\)\\)}\\)\[NoBreak] may contain \ significant numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.7289328188926487`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"General", "::", "stop"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Further output of \ \[NoBreak]\\!\\(\\*StyleBox[\\(LinearSolve :: luc\\), \\\"MessageName\\\"]\\)\ \[NoBreak] will be suppressed during this calculation. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/General/stop\\\", \ ButtonNote -> \\\"General::stop\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.7289328189096937`*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "3.1415918306351895`"}], ",", RowBox[{"{", RowBox[{"1.`", ",", RowBox[{"-", "0.3183099695665471`"}], ",", "0.1013212367254561`", ",", RowBox[{"-", "0.03225155977852484`"}], ",", "0.010265993011575913`"}], "}"}], ",", "4"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7289328227118177`*^9, 3.7289328227308598`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", "Approximation"}]}]}], " ", "of", " ", "the", " ", "next", " ", "least", " ", "dominant", " ", "eigenpair", " ", "by", " ", "HouseHolder", " ", "Deflation"}]], "Input", CellChangeTimes->{{3.7288327843009777`*^9, 3.7288328207636557`*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"InversePowerMethod", "[", RowBox[{"A", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.7288241902161283`*^9, 3.7288242031846294`*^9}, { 3.728824239105164*^9, 3.728824240024612*^9}, 3.7288256800643606`*^9, { 3.728827747279608*^9, 3.7288277481619277`*^9}, 3.7288277953635*^9, { 3.728828162713482*^9, 3.728828182935279*^9}, 3.7288282323430004`*^9, { 3.72892393428718*^9, 3.7289239384803104`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "0.09999999916353217`"}], ",", RowBox[{"{", RowBox[{"0.00009999999665413653`", ",", RowBox[{"-", "0.0009999999749059569`"}], ",", "0.009999999832706429`", ",", RowBox[{"-", "0.09999999916353217`"}], ",", "1.`"}], "}"}], ",", "16"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7289328367942753`*^9, 3.728932836811344*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"A2", "=", RowBox[{"HouseHolderDeflatedMatrix", "[", RowBox[{"A", ",", "t"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"%", "//", "MatrixForm"}]}], "Input", CellChangeTimes->{{3.7288318659339895`*^9, 3.728831901249915*^9}, { 3.728932475280542*^9, 3.728932485252043*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0.02243628193098516`", RowBox[{"-", "0.021871856048461837`"}], "0.0513126639540855`", RowBox[{"-", "1.0030238295656453`"}]}, {"0.7855860631179167`", "0.11922971843701016`", "0.48176180326012763`", "0.08135382540577123`"}, {"2.144139386755872`", RowBox[{"-", "0.19229719434328463`"}], RowBox[{"-", "4.817618072899105`"}], RowBox[{"-", "0.8135382608626986`"}]}, { RowBox[{"-", "21.44139404690908`"}], "11.922972043164673`", "49.1761811319693`", "8.135382676676846`"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.728932840602411*^9}] }, Open ]], Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", RowBox[{"n", "-", "1"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"InversePowerMethod", "[", RowBox[{"A2", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.7288241902161283`*^9, 3.7288242031846294`*^9}, { 3.728824239105164*^9, 3.728824240024612*^9}, 3.7288256800643606`*^9, { 3.728827747279608*^9, 3.7288277481619277`*^9}, 3.7288277953635*^9, { 3.728828162713482*^9, 3.728828182935279*^9}, 3.7288282323430004`*^9, { 3.7288328829500666`*^9, 3.728832886869494*^9}, {3.7289324958522425`*^9, 3.7289325009608617`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1.4142137232253484`"}], ",", RowBox[{"{", RowBox[{"0.6832023648518021`", ",", RowBox[{"-", "0.4715553126700384`"}], ",", "0.21802334548231175`", ",", "1.`"}], "}"}], ",", "200"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.728932855158129*^9, 3.7289328551782064`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"t", "=", RowBox[{"RandomReal", "[", RowBox[{"1", ",", "n"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"t", "/", RowBox[{"Norm", "[", RowBox[{"t", ",", "Infinity"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"lam", ",", "t", ",", "k"}], "}"}], "=", RowBox[{"InversePowerMethodImprove", "[", RowBox[{"A", ",", "lam", ",", "itmax", ",", " ", "toll", ",", "t"}], "]"}]}]}], "Input", CellChangeTimes->{{3.728828274199732*^9, 3.7288282854884624`*^9}, { 3.7288340958318524`*^9, 3.7288340970631585`*^9}, {3.728834168134203*^9, 3.7288341711121254`*^9}, 3.7288342073183403`*^9, {3.7288343446833487`*^9, 3.7288343461061583`*^9}, 3.728834444008589*^9, {3.7288347329001446`*^9, 3.728834733057583*^9}, {3.7289325067783103`*^9, 3.7289325124744916`*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LUDecomposition", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LUDecomposition\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({4.7736443282075545`, \ 21.5361216730038`, \\(\\(-11.850136239782016`\\)\\), \ \\(\\(-49.747899159663866`\\)\\), \\(\\(-4.835098335854766`\\)\\)}\\)\\), \\(\ \\({1.`, 1.4142137232253484`, 0.`, 0.`, 0.`}\\)\\), \\(\\({0.`, 1.`, \ 1.4142137232253484`, 0.`, 0.`}\\)\\), \\(\\({0.`, 0.`, 1.`, \ 1.4142137232253484`, 0.`}\\)\\), \\(\\({0.`, 0.`, 0.`, 1.`, \ 1.4142137232253484`}\\)\\)}\\)\[NoBreak] may contain significant numerical \ errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LUDecomposition::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.728932849736706*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({4.7736443282075545`, \ 21.5361216730038`, \\(\\(-11.850136239782016`\\)\\), \ \\(\\(-49.747899159663866`\\)\\), \\(\\(-4.835098335854766`\\)\\)}\\)\\), \\(\ \\({0.`, \\(\\(-3.09724967712613`\\)\\), 2.482408706019285`, \ 10.421366934629502`, 1.0128736041946147`}\\)\\), \\(\\({\\(\[LeftSkeleton] 1 \ \[RightSkeleton]\\)}\\)\\), \\(\\({0.`, 0.`, 0.`, 1.`, \ 1.4142137232253484`}\\)\\), \\(\\({0.`, 0.`, 0.`, 0.`, \ \\(\\(-8.881784197001252`*^-16\\)\\)}\\)\\)}\\)\[NoBreak] may contain \ significant numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.7289328497667856`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({4.7736443282075545`, \ 21.5361216730038`, \\(\\(-11.850136239782016`\\)\\), \ \\(\\(-49.747899159663866`\\)\\), \\(\\(-4.835098335854766`\\)\\)}\\)\\), \\(\ \\({0.`, \\(\\(-3.09724967712613`\\)\\), 2.482408706019285`, \ 10.421366934629502`, 1.0128736041946147`}\\)\\), \\(\\({\\(\[LeftSkeleton] 1 \ \[RightSkeleton]\\)}\\)\\), \\(\\({0.`, 0.`, 0.`, 1.`, \ 1.4142137232253484`}\\)\\), \\(\\({0.`, 0.`, 0.`, 0.`, \ \\(\\(-8.881784197001252`*^-16\\)\\)}\\)\\)}\\)\[NoBreak] may contain \ significant numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.7289328497948585`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"LinearSolve", "::", "luc"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Result for \[NoBreak]\\!\\(LinearSolve\\)\[NoBreak] of \ badly conditioned matrix \[NoBreak]\\!\\({\\(\\({4.7736443282075545`, \ 21.5361216730038`, \\(\\(-11.850136239782016`\\)\\), \ \\(\\(-49.747899159663866`\\)\\), \\(\\(-4.835098335854766`\\)\\)}\\)\\), \\(\ \\({0.`, \\(\\(-3.09724967712613`\\)\\), 2.482408706019285`, \ 10.421366934629502`, 1.0128736041946147`}\\)\\), \\(\\({\\(\[LeftSkeleton] 1 \ \[RightSkeleton]\\)}\\)\\), \\(\\({0.`, 0.`, 0.`, 1.`, \ 1.4142137232253484`}\\)\\), \\(\\({0.`, 0.`, 0.`, 0.`, \ \\(\\(-8.881784197001252`*^-16\\)\\)}\\)\\)}\\)\[NoBreak] may contain \ significant numerical errors. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/luc\\\", ButtonNote -> \ \\\"LinearSolve::luc\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.7289328498239627`*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"General", "::", "stop"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Further output of \ \[NoBreak]\\!\\(\\*StyleBox[\\(LinearSolve :: luc\\), \\\"MessageName\\\"]\\)\ \[NoBreak] will be suppressed during this calculation. \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/General/stop\\\", \ ButtonNote -> \\\"General::stop\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.728932849839026*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1.414213723225348`"}], ",", RowBox[{"{", RowBox[{"1.`", ",", RowBox[{"-", "0.70710670076043`"}], ",", "0.49999988626030045`", ",", RowBox[{"-", "0.35355326995411146`"}], ",", "0.2499998862603135`"}], "}"}], ",", "4"}], "}"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.7289328582523584`*^9, 3.7289328582724137`*^9}}] }, WindowSize->{692, 608}, WindowMargins->{{Automatic, -7}, {Automatic, -1}}, Magnification->1.4000000953674316`, FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (January 25, 2013)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[579, 22, 664, 11, 97, "Input"], Cell[1246, 35, 166, 2, 41, "Output"] }, Open ]], Cell[1427, 40, 178, 3, 42, "Input"], Cell[1608, 45, 360, 12, 42, "Input"], Cell[CellGroupData[{ Cell[1993, 61, 868, 23, 151, "Input"], Cell[2864, 86, 762, 21, 123, "Output"] }, Open ]], Cell[3641, 110, 346, 8, 70, "Input"], Cell[CellGroupData[{ Cell[4012, 122, 756, 18, 97, "Input"], Cell[4771, 142, 280, 7, 41, "Output"] }, Open ]], Cell[5066, 152, 351, 9, 124, "Input"], Cell[CellGroupData[{ Cell[5442, 165, 329, 7, 70, "Input"], Cell[5774, 174, 955, 25, 101, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6766, 204, 837, 21, 97, "Input"], Cell[7606, 227, 287, 8, 41, "Output"] }, Open ]], Cell[7908, 238, 370, 10, 124, "Input"], Cell[CellGroupData[{ Cell[8303, 252, 897, 20, 124, "Input"], Cell[9203, 274, 811, 14, 82, "Message"], Cell[10017, 290, 598, 11, 82, "Message"], Cell[10618, 303, 598, 11, 82, "Message"], Cell[11219, 316, 333, 9, 41, "Output"] }, Open ]], Cell[11567, 328, 396, 10, 124, "Input"], Cell[11966, 340, 321, 7, 70, "Input"], Cell[CellGroupData[{ Cell[12312, 351, 841, 19, 124, "Input"], Cell[13156, 372, 317, 8, 67, "Output"] }, Open ]], Cell[13488, 383, 384, 9, 124, "Input"], Cell[CellGroupData[{ Cell[13897, 396, 325, 7, 70, "Input"], Cell[14225, 405, 842, 19, 101, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[15104, 429, 927, 22, 124, "Input"], Cell[16034, 453, 308, 9, 41, "Output"] }, Open ]], Cell[16357, 465, 372, 10, 124, "Input"], Cell[CellGroupData[{ Cell[16754, 479, 899, 20, 124, "Input"], Cell[17656, 501, 811, 14, 82, "Message"], Cell[18470, 517, 873, 15, 123, "Message"], Cell[19346, 534, 875, 15, 123, "Message"], Cell[20224, 551, 875, 15, 123, "Message"], Cell[21102, 568, 559, 11, 57, "Message"] }, Open ]], Cell[21676, 582, 401, 10, 124, InheritFromParent], Cell[22080, 594, 403, 10, 124, "Input"], Cell[22486, 606, 391, 14, 42, "Input"], Cell[CellGroupData[{ Cell[22902, 624, 836, 23, 151, "Input"], Cell[23741, 649, 752, 21, 102, "Output"] }, Open ]], Cell[24508, 673, 346, 8, 70, "Input"], Cell[CellGroupData[{ Cell[24879, 685, 756, 18, 97, "Input"], Cell[25638, 705, 285, 7, 41, "Output"] }, Open ]], Cell[25938, 715, 351, 9, 124, "Input"], Cell[CellGroupData[{ Cell[26314, 728, 329, 7, 72, "Input"], Cell[26646, 737, 928, 23, 103, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[27611, 765, 837, 21, 100, "Input"], Cell[28451, 788, 291, 7, 43, "Output"] }, Open ]], Cell[28757, 798, 336, 8, 100, "Input"], Cell[CellGroupData[{ Cell[29118, 810, 897, 20, 100, "Input"], Cell[30018, 832, 855, 15, 29, "Message"], Cell[30876, 849, 908, 16, 40, "Message"], Cell[31787, 867, 906, 16, 40, "Message"], Cell[32696, 885, 323, 8, 43, "Output"] }, Open ]], Cell[33034, 896, 364, 9, 72, "Input"], Cell[33401, 907, 321, 7, 43, "Input"], Cell[CellGroupData[{ Cell[33747, 918, 841, 19, 100, "Input"], Cell[34591, 939, 354, 8, 43, "Output"] }, Open ]], Cell[34960, 950, 393, 9, 72, "Input"], Cell[CellGroupData[{ Cell[35378, 963, 325, 7, 72, "Input"], Cell[35706, 972, 865, 20, 103, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[36608, 997, 927, 22, 100, "Input"], Cell[37538, 1021, 290, 7, 43, "Output"] }, Open ]], Cell[37843, 1031, 332, 8, 72, "Input"], Cell[CellGroupData[{ Cell[38200, 1043, 899, 20, 100, "Input"], Cell[39102, 1065, 851, 15, 29, "Message"], Cell[39956, 1082, 896, 16, 40, "Message"], Cell[40855, 1100, 894, 16, 40, "Message"], Cell[41752, 1118, 896, 16, 40, "Message"], Cell[42651, 1136, 630, 12, 29, "Message"], Cell[43284, 1150, 320, 8, 121, "Output"] }, Open ]], Cell[43619, 1161, 364, 9, 72, "Input"], Cell[43986, 1172, 384, 12, 43, "Input"], Cell[CellGroupData[{ Cell[44395, 1188, 1041, 27, 72, "Input"], Cell[45439, 1217, 973, 29, 144, "Output"] }, Open ]], Cell[46427, 1249, 760, 14, 72, "Input"], Cell[47190, 1265, 346, 8, 43, "Input"], Cell[47539, 1275, 756, 18, 100, "Input"], Cell[48298, 1295, 385, 9, 72, "Input"], Cell[CellGroupData[{ Cell[48708, 1308, 329, 7, 72, "Input"], Cell[49040, 1317, 1090, 27, 106, "Output"] }, Open ]], Cell[50145, 1347, 837, 21, 100, "Input"], Cell[50985, 1370, 416, 10, 72, "Input"], Cell[CellGroupData[{ Cell[51426, 1384, 897, 20, 100, "Input"], Cell[52326, 1406, 938, 17, 78, "Message"], Cell[53267, 1425, 1007, 18, 119, "Message"], Cell[54277, 1445, 1007, 18, 119, "Message"], Cell[55287, 1465, 1007, 18, 119, "Message"], Cell[56297, 1485, 535, 11, 29, "Message"] }, Open ]], Cell[56847, 1499, 435, 10, 128, InheritFromParent], Cell[57285, 1511, 321, 7, 72, "Input"], Cell[57609, 1520, 841, 19, 100, "Input"], Cell[58453, 1541, 447, 11, 128, InheritFromParent], Cell[CellGroupData[{ Cell[58925, 1556, 325, 7, 72, "Input"], Cell[59253, 1565, 1136, 28, 126, "Output"] }, Open ]], Cell[60404, 1596, 927, 22, 100, "Input"], Cell[61334, 1620, 384, 9, 128, InheritFromParent], Cell[CellGroupData[{ Cell[61743, 1633, 899, 20, 100, "Input"], Cell[62645, 1655, 939, 17, 78, "Message"], Cell[63587, 1674, 1007, 18, 119, "Message"], Cell[64597, 1694, 1007, 18, 119, "Message"], Cell[65607, 1714, 1007, 18, 119, "Message"], Cell[66617, 1734, 533, 11, 29, "Message"] }, Open ]], Cell[67165, 1748, 431, 10, 100, InheritFromParent] } ] *) (* End of internal cache information *)