(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 13.1' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     40948,       1025]
NotebookOptionsPosition[     38625,        984]
NotebookOutlinePosition[     39072,       1002]
CellTagsIndexPosition[     39029,        999]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["\:4ee3\:7801", "Subsection",
 CellChangeTimes->{{3.924555227023057*^9, 
  3.9245552380596447`*^9}},ExpressionUUID->"0af2c2ea-193f-4649-a13d-\
0c6d54e22272"],

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", "\:5b9a\:4e49\:6709\:6548\:6570\:5b57\:51fd\:6570", "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"EffectiveDigits", "[", 
     RowBox[{"a_", ",", "b_"}], "]"}], ":=", 
    RowBox[{"Module", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
       "m", ",", "n", ",", "scientificA", ",", "base", ",", "exponent"}], 
       "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", 
      RowBox[{"(*", 
       RowBox[{
        RowBox[{
         RowBox[{
         "\:5c06a\:8f6c\:6362\:4e3a\:79d1\:5b66\:8bb0\:6570\:6cd5\:5f62\:5f0f\
", " ", "0.", "xyz"}], "..."}], "\[Times]", 
        RowBox[{"10", "^", "m"}]}], "*)"}], "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"scientificA", "=", 
        RowBox[{"MantissaExponent", "[", 
         RowBox[{"RealAbs", "[", "a", "]"}], "]"}]}], ";", 
       "\[IndentingNewLine]", 
       RowBox[{"base", "=", 
        RowBox[{"scientificA", "[", 
         RowBox[{"[", "1", "]"}], "]"}]}], ";", "\[IndentingNewLine]", 
       RowBox[{"exponent", "=", 
        RowBox[{"scientificA", "[", 
         RowBox[{"[", "2", "]"}], "]"}]}], ";", "\[IndentingNewLine]", 
       RowBox[{"m", "=", "exponent"}], ";", "\[IndentingNewLine]", 
       "\[IndentingNewLine]", 
       RowBox[{
       "(*", "\:627e\:5230\:6ee1\:8db3\:4e0d\:7b49\:5f0f\:7684\:6700\:5927\
\:7684n", "*)"}], "\[IndentingNewLine]", 
       RowBox[{"n", "=", 
        RowBox[{"Max", "[", 
         RowBox[{"0", ",", 
          RowBox[{"Floor", "[", 
           RowBox[{"m", "-", 
            RowBox[{"Log10", "[", 
             RowBox[{"2", " ", 
              RowBox[{"Abs", "[", 
               RowBox[{"a", "-", "b"}], "]"}]}], "]"}]}], "]"}]}], "]"}]}], 
       ";", "\[IndentingNewLine]", "\[IndentingNewLine]", 
       RowBox[{
       "(*", "\:8fd4\:56de\:6709\:6548\:6570\:5b57\:4f4d\:6570", "*)"}], 
       "\[IndentingNewLine]", "n"}]}], "\[IndentingNewLine]", "]"}]}], 
   ";"}]}]], "Input",
 CellChangeTimes->{{3.9251073293545046`*^9, 3.9251073526776114`*^9}, {
   3.925107410625913*^9, 3.9251074145765753`*^9}, 3.92510744585256*^9, {
   3.9251075602171364`*^9, 3.9251075689329004`*^9}, {3.9251076054553037`*^9, 
   3.9251076310428567`*^9}, {3.925107679326515*^9, 3.925107685315797*^9}, {
   3.9251077959428487`*^9, 
   3.925107810713959*^9}},ExpressionUUID->"8c29b7ad-df78-4904-86b4-\
d30b6a44c46b"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"GaussN", "[", "n_", "]"}], ":=", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"n", "^", "3"}], "+", 
      RowBox[{"3", 
       RowBox[{"n", "^", "2"}]}], "-", "n"}], ")"}], "/", "3"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
   3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
   3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
   3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
   3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
   3.9245640966207247`*^9, 3.9245641010009136`*^9}, 3.925107325009946*^9},
 CellLabel->"In[1]:=",ExpressionUUID->"d383ac27-2b85-4a1c-8f34-a880413b2a3f"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"PrincipalMinors", "[", "M_", "]"}], ":=", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"n", "=", 
        RowBox[{"Length", "[", "M", "]"}]}], ",", "minors"}], "}"}], ",", 
     RowBox[{
      RowBox[{"minors", "=", 
       RowBox[{"Table", "[", 
        RowBox[{
         RowBox[{"Det", "[", 
          RowBox[{"M", "[", 
           RowBox[{"[", 
            RowBox[{
             RowBox[{"1", ";;", "k"}], ",", 
             RowBox[{"1", ";;", "k"}]}], "]"}], "]"}], "]"}], ",", 
         RowBox[{"{", 
          RowBox[{"k", ",", "1", ",", "n"}], "}"}]}], "]"}]}], ";", 
      "minors"}]}], "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.924564112173971*^9}},
 CellLabel->"In[2]:=",ExpressionUUID->"d5cfeb24-8247-4e06-ac4e-99584add822b"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"LUDe", "[", "matrix_", "]"}], ":=", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"lu", ",", "perm", ",", "l", ",", "u", ",", "n"}], "}"}], ",", 
     RowBox[{
      RowBox[{
       RowBox[{"{", 
        RowBox[{"lu", ",", "perm"}], "}"}], "=", 
       RowBox[{
        RowBox[{"LUDecomposition", "[", "matrix", "]"}], "[", 
        RowBox[{"[", 
         RowBox[{"1", ";;", "2"}], "]"}], "]"}]}], ";", 
      RowBox[{
      "(*", "\:83b7\:53d6LU\:5206\:89e3\:7684LU\:77e9\:9635\:548c\:8f74\:5411\
\:91cf", "*)"}], "\[IndentingNewLine]", 
      RowBox[{"n", "=", 
       RowBox[{"Length", "[", "lu", "]"}]}], ";", 
      RowBox[{"(*", "\:77e9\:9635\:7684\:5927\:5c0f", "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"l", "=", 
       RowBox[{
        RowBox[{"LowerTriangularize", "[", 
         RowBox[{"lu", ",", 
          RowBox[{"-", "1"}]}], "]"}], "+", 
        RowBox[{"IdentityMatrix", "[", "n", "]"}]}]}], ";", 
      RowBox[{"(*", 
       RowBox[{
       "\:83b7\:53d6L\:77e9\:9635", "\:ff1a", 
        "LU\:77e9\:9635\:7684\:4e0b\:4e09\:89d2\:90e8\:5206\:52a0\:4e0a\:5355\
\:4f4d\:77e9\:9635\:7684\:5bf9\:89d2\:7ebf"}], "*)"}], "\[IndentingNewLine]", 
      RowBox[{"u", "=", 
       RowBox[{"UpperTriangularize", "[", "lu", "]"}]}], ";", 
      RowBox[{"(*", 
       RowBox[{
       "\:83b7\:53d6U\:77e9\:9635", "\:ff1a", 
        "LU\:77e9\:9635\:7684\:4e0a\:4e09\:89d2\:90e8\:5206"}], "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"Map", "[", 
       RowBox[{"MatrixForm", ",", 
        RowBox[{"{", 
         RowBox[{"l", ",", "u"}], "}"}]}], "]"}]}]}], 
    RowBox[{
    "(*", "\:8fd4\:56de\:5305\:542bL\:548cU\:7684\:5217\:8868", "*)"}], 
    "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.9245641245795727`*^9}},
 CellLabel->"In[3]:=",ExpressionUUID->"09cbb4b3-a43f-4430-aff6-bc0592dba7aa"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"ChDe", "[", "A_", "]"}], ":=", 
   RowBox[{
    RowBox[{"Transpose", "[", 
     RowBox[{"CholeskyDecomposition", "[", "A", "]"}], "]"}], "//", 
    "MatrixForm"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.9245641294390497`*^9}},
 CellLabel->"In[4]:=",ExpressionUUID->"55d18b28-5e77-464d-841c-e533675bb9e2"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"PrincipalMinors", "[", "M_", "]"}], ":=", 
    RowBox[{"Module", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"n", "=", 
         RowBox[{"Length", "[", "M", "]"}]}], ",", "minors"}], "}"}], ",", 
      RowBox[{
       RowBox[{"minors", "=", 
        RowBox[{"Table", "[", 
         RowBox[{
          RowBox[{"Det", "[", 
           RowBox[{"M", "[", 
            RowBox[{"[", 
             RowBox[{
              RowBox[{"1", ";;", "k"}], ",", 
              RowBox[{"1", ";;", "k"}]}], "]"}], "]"}], "]"}], ",", 
          RowBox[{"{", 
           RowBox[{"k", ",", "1", ",", "n"}], "}"}]}], "]"}]}], ";", 
       "minors"}]}], "]"}]}], ";"}], 
  RowBox[{
  "(*", "\:8fd4\:56deM\:7684\:5404\:9636\:987a\:5e8f\:4e3b\:5b50\:5f0f", 
   "*)"}]}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.924564135113705*^9}},
 CellLabel->"In[5]:=",ExpressionUUID->"cad63f8b-e1a7-4ea9-8cbc-d8ef3fddddb2"],

Cell[BoxData[
 RowBox[{
  RowBox[{
  "(*", "\:9002\:7528\:4e8e\:4e09\:5bf9\:89d2\:77e9\:9635\:7684Crout\:5206\
\:89e3", "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"CroutDe", "[", "matrix_", "]"}], ":=", 
    RowBox[{"Module", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"n", "=", 
         RowBox[{"Length", "[", "matrix", "]"}]}], ",", "l", ",", "u"}], 
       "}"}], ",", 
      RowBox[{
       RowBox[{"l", "=", 
        RowBox[{"LowerTriangularize", "[", "matrix", "]"}]}], ";", 
       "\[IndentingNewLine]", 
       RowBox[{"u", "=", 
        RowBox[{"UpperTriangularize", "[", 
         RowBox[{"IdentityMatrix", "[", "n", "]"}], "]"}]}], ";", 
       RowBox[{"(*", "\:5355\:4f4d\:4e0a\:4e09\:89d2\:77e9\:9635", "*)"}], 
       "\[IndentingNewLine]", 
       RowBox[{"(*", 
        RowBox[{
        "\:586b\:5145", " ", "L", " ", "\:548c", " ", "U", " ", 
         "\:7684\:5143\:7d20"}], "*)"}], 
       RowBox[{"Do", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"l", "[", 
             RowBox[{"[", 
              RowBox[{"i", ",", "i"}], "]"}], "]"}], "=", 
            RowBox[{
             RowBox[{"matrix", "[", 
              RowBox[{"[", 
               RowBox[{"i", ",", "i"}], "]"}], "]"}], "-", 
             RowBox[{"Sum", "[", 
              RowBox[{
               RowBox[{
                RowBox[{"l", "[", 
                 RowBox[{"[", 
                  RowBox[{"i", ",", "k"}], "]"}], "]"}], 
                RowBox[{"u", "[", 
                 RowBox[{"[", 
                  RowBox[{"k", ",", "i"}], "]"}], "]"}]}], ",", 
               RowBox[{"{", 
                RowBox[{"k", ",", "1", ",", 
                 RowBox[{"i", "-", "1"}]}], "}"}]}], "]"}]}]}], ",", 
           RowBox[{"If", "[", 
            RowBox[{
             RowBox[{"i", "<", "n"}], ",", 
             RowBox[{
              RowBox[{
               RowBox[{"u", "[", 
                RowBox[{"[", 
                 RowBox[{"i", ",", 
                  RowBox[{"i", "+", "1"}]}], "]"}], "]"}], "=", 
               RowBox[{
                RowBox[{"matrix", "[", 
                 RowBox[{"[", 
                  RowBox[{"i", ",", 
                   RowBox[{"i", "+", "1"}]}], "]"}], "]"}], "/", 
                RowBox[{"l", "[", 
                 RowBox[{"[", 
                  RowBox[{"i", ",", "i"}], "]"}], "]"}]}]}], ";", 
              "\[IndentingNewLine]", 
              RowBox[{
               RowBox[{"l", "[", 
                RowBox[{"[", 
                 RowBox[{
                  RowBox[{"i", "+", "1"}], ",", "i"}], "]"}], "]"}], "=", 
               RowBox[{
                RowBox[{"matrix", "[", 
                 RowBox[{"[", 
                  RowBox[{
                   RowBox[{"i", "+", "1"}], ",", "i"}], "]"}], "]"}], "-", 
                RowBox[{"Sum", "[", 
                 RowBox[{
                  RowBox[{
                   RowBox[{"l", "[", 
                    RowBox[{"[", 
                    RowBox[{
                    RowBox[{"i", "+", "1"}], ",", "k"}], "]"}], "]"}], " ", 
                   RowBox[{"u", "[", 
                    RowBox[{"[", 
                    RowBox[{"k", ",", "i"}], "]"}], "]"}]}], ",", 
                  RowBox[{"{", 
                   RowBox[{"k", ",", "1", ",", 
                    RowBox[{"i", "-", "1"}]}], "}"}]}], "]"}]}]}]}]}], 
            "]"}]}], "}"}], ",", 
         RowBox[{"{", 
          RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ";", 
       "\[IndentingNewLine]", 
       RowBox[{"MatrixForm", "/@", 
        RowBox[{"{", 
         RowBox[{"l", ",", "u"}], "}"}]}]}]}], "]"}]}], ";"}]}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.9245641505664206`*^9}},
 CellLabel->"In[6]:=",ExpressionUUID->"05acbbc3-479c-4e50-a4dc-aaf84550f6e8"],

Cell[BoxData[
 RowBox[{
  RowBox[{
  "(*", "\:9002\:7528\:4e8e\:4e00\:822c\:77e9\:9635\:7684Crout\:5206\:89e3", 
   "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"CroutDeCo", "[", "matrix_", "]"}], ":=", 
    RowBox[{"Module", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"n", "=", 
         RowBox[{"Length", "[", "matrix", "]"}]}], ",", "l", ",", "u", ",", 
        "sum"}], "}"}], ",", 
      RowBox[{
       RowBox[{"l", "=", 
        RowBox[{"ConstantArray", "[", 
         RowBox[{"0", ",", 
          RowBox[{"{", 
           RowBox[{"n", ",", "n"}], "}"}]}], "]"}]}], ";", 
       "\[IndentingNewLine]", 
       RowBox[{"u", "=", 
        RowBox[{"IdentityMatrix", "[", "n", "]"}]}], ";", 
       RowBox[{"(*", "\:5355\:4f4d\:4e0a\:4e09\:89d2\:77e9\:9635", "*)"}], 
       RowBox[{"Do", "[", 
        RowBox[{"(*", 
         RowBox[{
         "\:8ba1\:7b97", " ", "l", " ", "\:7684\:7b2c", " ", "i", " ", 
          "\:884c\:548c", " ", "u", " ", "\:7684\:7b2c", " ", "i", " ", 
          "\:5217"}], "*)"}], 
        RowBox[{
         RowBox[{
          RowBox[{"Do", "[", 
           RowBox[{"(*", 
            RowBox[{"\:8ba1\:7b97", " ", "l", " ", "\:7684\:5143\:7d20"}], 
            "*)"}], 
           RowBox[{
            RowBox[{
             RowBox[{"sum", "=", 
              RowBox[{"Sum", "[", 
               RowBox[{
                RowBox[{
                 RowBox[{"l", "[", 
                  RowBox[{"[", 
                   RowBox[{"i", ",", "k"}], "]"}], "]"}], " ", 
                 RowBox[{"u", "[", 
                  RowBox[{"[", 
                   RowBox[{"k", ",", "j"}], "]"}], "]"}]}], ",", 
                RowBox[{"{", 
                 RowBox[{"k", ",", "1", ",", 
                  RowBox[{
                   RowBox[{"Min", "[", 
                    RowBox[{"i", ",", "j"}], "]"}], "-", "1"}]}], "}"}]}], 
               "]"}]}], ";", "\[IndentingNewLine]", 
             RowBox[{"If", "[", 
              RowBox[{
               RowBox[{"i", ">=", "j"}], ",", 
               RowBox[{
                RowBox[{"l", "[", 
                 RowBox[{"[", 
                  RowBox[{"i", ",", "j"}], "]"}], "]"}], "=", 
                RowBox[{
                 RowBox[{"matrix", "[", 
                  RowBox[{"[", 
                   RowBox[{"i", ",", "j"}], "]"}], "]"}], "-", "sum"}]}]}], 
              "]"}]}], ",", 
            RowBox[{"{", 
             RowBox[{"j", ",", "1", ",", "n"}], "}"}]}], "]"}], ";", 
          "\[IndentingNewLine]", 
          RowBox[{"Do", "[", 
           RowBox[{"(*", 
            RowBox[{
             RowBox[{"\:8ba1\:7b97", " ", "u", " ", "\:7684\:5143\:7d20"}], 
             "\:ff0c", 
             "\:53ea\:8ba1\:7b97\:975e\:5bf9\:89d2\:7ebf\:5143\:7d20", 
             "\:ff0c", "\:5bf9\:89d2\:7ebf\:5143\:7d20\:5df2\:8bbe\:4e3a1"}], 
            "*)"}], 
           RowBox[{
            RowBox[{"If", "[", 
             RowBox[{
              RowBox[{"j", ">", "i"}], ",", 
              RowBox[{
               RowBox[{"sum", "=", 
                RowBox[{"Sum", "[", 
                 RowBox[{
                  RowBox[{
                   RowBox[{"l", "[", 
                    RowBox[{"[", 
                    RowBox[{"i", ",", "k"}], "]"}], "]"}], " ", 
                   RowBox[{"u", "[", 
                    RowBox[{"[", 
                    RowBox[{"k", ",", "j"}], "]"}], "]"}]}], ",", 
                  RowBox[{"{", 
                   RowBox[{"k", ",", "1", ",", 
                    RowBox[{"i", "-", "1"}]}], "}"}]}], "]"}]}], ";", 
               "\[IndentingNewLine]", 
               RowBox[{
                RowBox[{"u", "[", 
                 RowBox[{"[", 
                  RowBox[{"i", ",", "j"}], "]"}], "]"}], "=", 
                RowBox[{
                 RowBox[{"(", 
                  RowBox[{
                   RowBox[{"matrix", "[", 
                    RowBox[{"[", 
                    RowBox[{"i", ",", "j"}], "]"}], "]"}], "-", "sum"}], 
                  ")"}], "/", 
                 RowBox[{"l", "[", 
                  RowBox[{"[", 
                   RowBox[{"i", ",", "i"}], "]"}], "]"}]}]}]}]}], "]"}], ",", 
            RowBox[{"{", 
             RowBox[{"j", ",", "1", ",", "n"}], "}"}]}], "]"}]}], ",", 
         RowBox[{"{", 
          RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ";", 
       "\[IndentingNewLine]", 
       RowBox[{"MatrixForm", "/@", 
        RowBox[{"{", 
         RowBox[{"l", ",", "u"}], "}"}]}]}]}], "]"}]}], ";"}]}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.92456415596951*^9}},
 CellLabel->"In[7]:=",ExpressionUUID->"cf7097dc-67d2-4f27-a92e-0d3cdf2673ba"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"PBJ", "[", "A_", "]"}], ":=", 
   RowBox[{"Max", "[", 
    RowBox[{"Abs", "[", 
     RowBox[{"Eigenvalues", "[", "A", "]"}], "]"}], "]"}]}], 
  RowBox[{"(*", "\:8c31\:534a\:5f84", "*)"}], ";"}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.924564160023576*^9}},
 CellLabel->"In[8]:=",ExpressionUUID->"61610133-11de-4935-a818-8eab399e0a08"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Cond", "[", 
    RowBox[{"A_", ",", "p_"}], "]"}], ":=", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"normA", ",", "normInvA"}], "}"}], ",", 
     RowBox[{
      RowBox[{"normA", "=", 
       RowBox[{"Norm", "[", 
        RowBox[{"A", ",", "p"}], "]"}]}], ";", 
      RowBox[{"(*", "\:8ba1\:7b97\:77e9\:9635A\:7684p\:8303\:6570", "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"normInvA", "=", 
       RowBox[{"Norm", "[", 
        RowBox[{
         RowBox[{"Inverse", "[", "A", "]"}], ",", "p"}], "]"}]}], ";", 
      RowBox[{
      "(*", "\:8ba1\:7b97\:77e9\:9635A\:9006\:7684p\:8303\:6570", "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"normA", "*", "normInvA"}]}]}], " ", 
    RowBox[{"(*", "\:8fd4\:56de\:6761\:4ef6\:6570", "*)"}], "]"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.924564163686198*^9}},
 CellLabel->"In[9]:=",ExpressionUUID->"8330e8f6-05cf-4d38-982e-97240a3d449f"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Jacobi", "[", "A_", "]"}], ":=", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"DD", ",", "L", ",", "U", ",", "n"}], "}"}], ",", 
     RowBox[{
      RowBox[{"n", "=", 
       RowBox[{"Length", "[", "A", "]"}]}], ";", 
      RowBox[{"(*", "\:83b7\:53d6\:77e9\:9635\:7684\:5927\:5c0f", "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"DD", "=", 
       RowBox[{"DiagonalMatrix", "[", 
        RowBox[{"Diagonal", "[", "A", "]"}], "]"}]}], ";", 
      RowBox[{"(*", 
       RowBox[{"\:6784\:9020\:5bf9\:89d2\:77e9\:9635", " ", "DD"}], "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"L", "=", 
       RowBox[{"-", 
        RowBox[{"LowerTriangularize", "[", 
         RowBox[{"A", ",", 
          RowBox[{"-", "1"}]}], "]"}]}]}], ";", 
      RowBox[{"(*", 
       RowBox[{
       "\:83b7\:53d6\:4e0b\:4e09\:89d2\:90e8\:5206", "\:ff0c", 
        "\:5e76\:53d6\:8d1f\:6570", "\:ff0c", 
        "\:5bf9\:89d2\:7ebf\:53ca\:4ee5\:4e0a\:5143\:7d20\:4e3a0"}], "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"U", "=", 
       RowBox[{"-", 
        RowBox[{"UpperTriangularize", "[", 
         RowBox[{"A", ",", "1"}], "]"}]}]}], ";", 
      RowBox[{"(*", 
       RowBox[{
       "\:83b7\:53d6\:4e0a\:4e09\:89d2\:90e8\:5206", "\:ff0c", 
        "\:5e76\:53d6\:8d1f\:6570", "\:ff0c", 
        "\:5bf9\:89d2\:7ebf\:53ca\:4ee5\:4e0b\:5143\:7d20\:4e3a0"}], "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{
        RowBox[{"Inverse", "[", "DD", "]"}], ".", 
        RowBox[{"(", 
         RowBox[{"L", "+", "U"}], ")"}]}], "//", "MatrixForm"}]}]}], " ", 
    RowBox[{
    "(*", "\:8ba1\:7b97\:8fed\:4ee3\:77e9\:9635\:5e76\:8fd4\:56de", "*)"}], 
    "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.9245641683775*^9}},
 CellLabel->"In[10]:=",ExpressionUUID->"31fd9b80-da51-4399-8d6d-7a7a95dedde9"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"GS", "[", "A_", "]"}], ":=", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"DD", ",", "L", ",", "U", ",", "n"}], "}"}], ",", 
     RowBox[{
      RowBox[{"n", "=", 
       RowBox[{"Length", "[", "A", "]"}]}], ";", 
      RowBox[{"(*", "\:83b7\:53d6\:77e9\:9635\:7684\:5927\:5c0f", "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"DD", "=", 
       RowBox[{"DiagonalMatrix", "[", 
        RowBox[{"Diagonal", "[", "A", "]"}], "]"}]}], ";", 
      RowBox[{"(*", 
       RowBox[{"\:6784\:9020\:5bf9\:89d2\:77e9\:9635", " ", "DD"}], "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"L", "=", 
       RowBox[{"-", 
        RowBox[{"LowerTriangularize", "[", 
         RowBox[{"A", ",", 
          RowBox[{"-", "1"}]}], "]"}]}]}], ";", 
      RowBox[{"(*", 
       RowBox[{
       "\:83b7\:53d6\:4e0b\:4e09\:89d2\:90e8\:5206", "\:ff0c", 
        "\:5e76\:53d6\:8d1f\:6570", "\:ff0c", 
        "\:5bf9\:89d2\:7ebf\:53ca\:4ee5\:4e0a\:5143\:7d20\:4e3a0"}], "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"U", "=", 
       RowBox[{"-", 
        RowBox[{"UpperTriangularize", "[", 
         RowBox[{"A", ",", "1"}], "]"}]}]}], ";", 
      RowBox[{"(*", 
       RowBox[{
       "\:83b7\:53d6\:4e0a\:4e09\:89d2\:90e8\:5206", "\:ff0c", 
        "\:5e76\:53d6\:8d1f\:6570", "\:ff0c", 
        "\:5bf9\:89d2\:7ebf\:53ca\:4ee5\:4e0b\:5143\:7d20\:4e3a0"}], "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{
        RowBox[{"Inverse", "[", 
         RowBox[{"DD", "-", "L"}], "]"}], ".", "U"}], "//", 
       "MatrixForm"}]}]}], 
    RowBox[{
    "(*", "\:8ba1\:7b97\:8fed\:4ee3\:77e9\:9635\:5e76\:8fd4\:56de", "*)"}], 
    "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.924564175395494*^9}},
 CellLabel->"In[11]:=",ExpressionUUID->"9427686b-95f7-4bb3-8dd3-6608b56a43f5"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"IsStrictlyDiagonallyDominant", "[", "matrix_", "]"}], ":=", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"n", "=", 
        RowBox[{"Length", "[", "matrix", "]"}]}], ",", "rowSum", ",", 
       "diagElem"}], "}"}], ",", 
     RowBox[{"And", "@@", 
      RowBox[{"Table", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"diagElem", "=", 
          RowBox[{"Abs", "[", 
           RowBox[{"matrix", "[", 
            RowBox[{"[", 
             RowBox[{"i", ",", "i"}], "]"}], "]"}], "]"}]}], ";", 
         "\[IndentingNewLine]", 
         RowBox[{"rowSum", "=", 
          RowBox[{
           RowBox[{"Total", "[", 
            RowBox[{"Abs", "[", 
             RowBox[{"matrix", "[", 
              RowBox[{"[", "i", "]"}], "]"}], "]"}], "]"}], "-", 
           "diagElem"}]}], ";", "\[IndentingNewLine]", 
         RowBox[{"diagElem", ">", "rowSum"}]}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}]}]}], "]"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.924564178263303*^9}},
 CellLabel->"In[12]:=",ExpressionUUID->"80e75e01-3f0c-4715-9e1d-a52d41219a4a"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"SOR", "[", 
    RowBox[{"M_", ",", "w_"}], "]"}], ":=", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"DD", ",", "L", ",", "U", ",", "n"}], "}"}], ",", 
     RowBox[{
      RowBox[{"n", "=", 
       RowBox[{"Length", "[", "M", "]"}]}], ";", 
      RowBox[{"(*", "\:83b7\:53d6\:77e9\:9635\:7684\:5927\:5c0f", "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"DD", "=", 
       RowBox[{"DiagonalMatrix", "[", 
        RowBox[{"Diagonal", "[", "M", "]"}], "]"}]}], ";", 
      RowBox[{"(*", 
       RowBox[{"\:6784\:9020\:5bf9\:89d2\:77e9\:9635", " ", "DD"}], "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"L", "=", 
       RowBox[{"-", 
        RowBox[{"LowerTriangularize", "[", 
         RowBox[{"M", ",", 
          RowBox[{"-", "1"}]}], "]"}]}]}], ";", 
      RowBox[{"(*", 
       RowBox[{
       "\:83b7\:53d6\:4e0b\:4e09\:89d2\:90e8\:5206", "\:ff0c", 
        "\:5e76\:53d6\:8d1f\:6570", "\:ff0c", 
        "\:5bf9\:89d2\:7ebf\:53ca\:4ee5\:4e0a\:5143\:7d20\:4e3a0"}], "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"U", "=", 
       RowBox[{"-", 
        RowBox[{"UpperTriangularize", "[", 
         RowBox[{"M", ",", "1"}], "]"}]}]}], ";", 
      RowBox[{"(*", 
       RowBox[{
       "\:83b7\:53d6\:4e0a\:4e09\:89d2\:90e8\:5206", "\:ff0c", 
        "\:5e76\:53d6\:8d1f\:6570", "\:ff0c", 
        "\:5bf9\:89d2\:7ebf\:53ca\:4ee5\:4e0b\:5143\:7d20\:4e3a0"}], "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{
        RowBox[{"Inverse", "[", 
         RowBox[{"DD", "-", 
          RowBox[{"w", " ", "L"}]}], "]"}], ".", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           RowBox[{"(", 
            RowBox[{"1", "-", "w"}], ")"}], " ", "DD"}], "+", 
          RowBox[{"w", " ", "U"}]}], ")"}]}], "//", "MatrixForm"}]}]}], " ", 
    RowBox[{
    "(*", "\:8ba1\:7b97SOR\:8fed\:4ee3\:77e9\:9635\:5e76\:8fd4\:56de", "*)"}],
     "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.9245641818996167`*^9}},
 CellLabel->"In[13]:=",ExpressionUUID->"cae67269-c439-4e79-a488-ef1787d38305"],

Cell[BoxData["\[IndentingNewLine]"], "Input",
 CellChangeTimes->{{3.9245553336596575`*^9, 3.9245553824883013`*^9}, {
  3.9245554141731977`*^9, 3.924555415332567*^9}, {3.9245554696079297`*^9, 
  3.9245554972859306`*^9}, {3.9245555282750926`*^9, 3.924555547281943*^9}, {
  3.9245637628267827`*^9, 3.924563812862997*^9}, {3.9245638757069693`*^9, 
  3.9245638767054405`*^9}, {3.924563928311846*^9, 3.9245639301632156`*^9}, {
  3.9245640966207247`*^9, 3.9245641818996167`*^9}},
 CellLabel->"In[14]:=",ExpressionUUID->"35a98b0b-7f78-42ba-bedd-e7f6867bf3df"]
}, Open  ]],

Cell[CellGroupData[{

Cell["\:51fd\:6570\:6587\:6863", "Subsection",
 CellChangeTimes->{
  3.924555241757887*^9},ExpressionUUID->"8c053a0e-ae75-4d2b-a257-\
96c36d9e4df0"],

Cell[BoxData[{
 RowBox[{"\:6c42\:7528\:8fd1\:4f3c\:503ca\:6765\:8fd1\:4f3c\:7cbe\:786e\:503c\
b\:7684\:6709\:6548\:6570\:5b57\:4f4d\:6570", "\:ff1a", 
  StyleBox[
   RowBox[{"EffectiveDigits", "[", 
    RowBox[{"a", ",", "b"}], "]"}],
   FontWeight->"Bold"]}], "\[IndentingNewLine]", 
 RowBox[{"\:7edf\:8ba1\:987a\:5e8fGauss\:6d88\:53bb\:6cd5\:7684\:4e58\:9664\
\:6cd5\:8ba1\:7b97\:6b21\:6570", "\:ff1a", 
  StyleBox[
   RowBox[{"GaussN", "[", "n", "]"}],
   FontWeight->"Bold"], "\:ff0c", 
  "n\:4e3a\:7ebf\:6027\:65b9\:7a0b\:7ec4\:7684\:672a\:77e5\:6570\:4e2a\:6570"}\
], "\n", 
 RowBox[{"LU\:5206\:89e3", "\:ff1a", 
  StyleBox[
   RowBox[{"LUDe", "[", "M", "]"}],
   FontWeight->"Bold"], "\:ff0c", 
  RowBox[{"\:8fd4\:56de", 
   RowBox[{"{", 
    RowBox[{"L", ",", "U"}], "}"}]}], "\:ff0c", 
  "L\:4e3a\:5355\:4f4d\:4e0b\:4e09\:89d2\:77e9\:9635", "\:ff0c", 
  "U\:4e3a\:4e0a\:4e09\:89d2\:77e9\:9635"}], "\n", 
 RowBox[{"Cholesky\:5206\:89e3", "\:ff1a", 
  StyleBox[
   RowBox[{"ChDe", "[", "M", "]"}],
   FontWeight->"Bold"], "\:ff0c", "\:63a5\:6536\:4e00\:4e2a\:77e9\:9635M", 
  "\:ff0c", 
  RowBox[{
  "\:628aM\:5206\:89e3\:4e3a\:4e00\:4e2a\:4e0b\:4e09\:89d2\:77e9\:9635G\:548c\
\:5176\:8f6c\:7f6e", 
   FormBox[
    SuperscriptBox["G", "T"],
    TraditionalForm], "\:7684\:4e58\:79ef"}], "\:ff0c", 
  RowBox[{"\:5373", 
   FormBox[
    RowBox[{"M", "=", 
     SuperscriptBox["GG", "T"]}],
    TraditionalForm]}], "\:ff0c", "\:8fd4\:56deG"}], "\n", 
 RowBox[{"\:5224\:5b9a\:662f\:5426\:4e3a\:6b63\:5b9a\:77e9\:9635", "\:ff1a", 
  StyleBox[
   RowBox[{"PositiveDefiniteMatrixQ", "[", "A", "]"}],
   FontWeight->"Bold"]}], "\n", 
 RowBox[{"\:6c42\:5404\:9636\:987a\:5e8f\:4e3b\:5b50\:5f0f", "\:ff1a", 
  StyleBox[
   RowBox[{"PrincipalMinors", "[", "A", "]"}],
   FontWeight->"Bold"]}], "\n", 
 RowBox[{
  RowBox[{"\:4e09\:5bf9\:89d2\:77e9\:9635\:7684Crout\:5206\:89e3", 
   RowBox[{"\:ff08", 
    RowBox[{
    "\:6548\:7387\:66f4\:5feb", "\:ff0c", 
     "\:53ea\:80fd\:7528\:4e8e\:4e09\:5bf9\:89d2\:77e9\:9635"}], "\:ff09"}]}],
   "\:ff1a", 
  StyleBox[
   RowBox[{"CroutDe", "[", "A", "]"}],
   FontWeight->"Bold"], "\:ff0c", 
  "\:8fd4\:56de\:4e00\:4e2a\:4e0b\:4e09\:89d2\:77e9\:9635\:548c\:4e00\:4e2a\
\:5355\:4f4d\:4e0a\:4e09\:89d2\:77e9\:9635"}], "\[IndentingNewLine]", 
 RowBox[{"\:666e\:901a\:77e9\:9635\:7684Crout\:5206\:89e3", "\:ff1a", 
  StyleBox[
   RowBox[{"CroutDeCo", "[", "A", "]"}],
   FontWeight->"Bold"], "\:ff0c", 
  "\:8fd4\:56de\:4e00\:4e2a\:4e0b\:4e09\:89d2\:77e9\:9635\:548c\:4e00\:4e2a\
\:5355\:4f4d\:4e0a\:4e09\:89d2\:77e9\:9635"}], "\n", 
 RowBox[{"\:5411\:91cf\:6216\:77e9\:9635\:7684\:8303\:6570", "\:ff1a", 
  StyleBox[
   RowBox[{"Norm", "[", 
    RowBox[{"A", ",", "p"}], "]"}],
   FontWeight->"Bold"], "\:ff0c", "p\:53ef\:4ee5\:4e3a1", ",", "2", ",", 
  "Infinity", ",", 
  RowBox[{"\"\<Frobenius\>\"", 
   RowBox[{"\:ff08", 
    RowBox[{"F", "-", "\:8303\:6570"}], "\:ff09"}]}]}], "\n", 
 RowBox[{"\:6c42\:77e9\:9635\:7684\:8c31\:534a\:5f84", "\:ff1a", 
  StyleBox[
   RowBox[{"PBJ", "[", "A", "]"}],
   FontWeight->"Bold"]}], "\n", 
 RowBox[{"\:6c42\:77e9\:9635\:7684p\:6761\:4ef6\:6570", "\:ff1a", 
  StyleBox[
   RowBox[{"Cond", "[", 
    RowBox[{"A", ",", "p"}], "]"}],
   FontWeight->"Bold"]}], "\n", 
 RowBox[{"\:6c42Jacobi\:8fed\:4ee3\:6cd5\:7684\:8fed\:4ee3\:77e9\:9635", 
  "\:ff1a", 
  StyleBox[
   RowBox[{"Jacobi", "[", "A", "]"}],
   FontWeight->"Bold"]}], "\n", 
 RowBox[{"\:6c42GS\:8fed\:4ee3\:6cd5\:7684\:8fed\:4ee3\:77e9\:9635", "\:ff1a", 
  StyleBox[
   RowBox[{"GS", "[", "A", "]"}],
   FontWeight->"Bold"]}], "\n", 
 RowBox[{"\:5224\:5b9a\:77e9\:9635\:662f\:5426\:4e25\:683c\:5bf9\:89d2\:5360\
\:4f18", "\:ff1a", 
  StyleBox[
   RowBox[{"IsStrictlyDiagonallyDominant", "[", "A", "]"}],
   FontWeight->"Bold"]}], "\n", 
 RowBox[{"\:6c42SOR\:65b9\:6cd5\:7684\:8fed\:4ee3\:77e9\:9635", "\:ff1a", 
  StyleBox[
   RowBox[{"SOR", "[", 
    RowBox[{"A", ",", "w"}], "]"}],
   FontWeight->"Bold"], "\:ff0c", 
  "w\:4e3a\:677e\:5f1b\:56e0\:5b50"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"QR\:5206\:89e3", "\:ff1a", 
   StyleBox[
    RowBox[{"QRDecomposition", "[", "M", "]"}],
    FontWeight->"Bold"], "\:ff0c", 
   "\:8fd4\:56de\:4e00\:4e2a\:6b63\:4ea4\:77e9\:9635\:548c\:4e00\:4e2a\:4e0a\
\:4e09\:89d2\:77e9\:9635"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  StyleBox[
   RowBox[{"\:8bf7\:5148", 
    StyleBox["\:8ba1\:7b97\:7b14\:8bb0\:672c",
     FontWeight->"Bold",
     FontColor->RGBColor[1., 0., 0.]]}]], "\:ff0c", 
  "\:7136\:540e\:5728\:4e0b\:9762\:7684\:4ee3\:7801\:533a\:57df\:4f7f\:7528\
\:4e0a\:8ff0\:51fd\:6570", "\:ff1a"}]}], "Text",
 CellChangeTimes->{{3.9245552533653126`*^9, 3.924555320850746*^9}, {
   3.924564662669675*^9, 3.9245646830186796`*^9}, {3.924564758396234*^9, 
   3.924564795234249*^9}, {3.9245665699632225`*^9, 3.9245665984255333`*^9}, {
   3.9250935894417396`*^9, 3.9250936431895814`*^9}, {3.9250937757510953`*^9, 
   3.9250937803540096`*^9}, {3.925107746562063*^9, 3.9251077733268404`*^9}, 
   3.9251078250537634`*^9},ExpressionUUID->"b16b1ea4-cce2-4a2b-92e1-\
4cba1822d789"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"MatrixForm", "/@", 
  RowBox[{"QRDecomposition", "[", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"1", ",", "3", ",", "2"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"3", ",", "7", ",", "5"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"4", ",", "3", ",", "6"}], "}"}]}], "}"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.9250936030389614`*^9, 3.9250936139902987`*^9}, {
   3.925093647590356*^9, 3.9250936484560027`*^9}, {3.92509886150305*^9, 
   3.925098878633748*^9}, {3.9250993167303553`*^9, 3.92509931843845*^9}, {
   3.9250994233264294`*^9, 3.925099427631544*^9}, {3.9251073673601284`*^9, 
   3.925107374212509*^9}, {3.925107691377334*^9, 3.925107738600565*^9}, 
   3.925107836400502*^9, {3.9251081795700912`*^9, 3.925108203832847*^9}},
 CellLabel->"In[43]:=",ExpressionUUID->"6602253a-4119-44c0-bc64-e5d9454a8813"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {
        FractionBox["1", 
         SqrtBox["26"]], 
        FractionBox["3", 
         SqrtBox["26"]], 
        RowBox[{"2", " ", 
         SqrtBox[
          FractionBox["2", "13"]]}]},
       {
        FractionBox["21", 
         SqrtBox["2899"]], 
        FractionBox["37", 
         SqrtBox["2899"]], 
        RowBox[{"-", 
         FractionBox["33", 
          SqrtBox["2899"]]}]},
       {
        FractionBox["19", 
         SqrtBox["446"]], 
        RowBox[{"-", 
         FractionBox["9", 
          SqrtBox["446"]]}], 
        SqrtBox[
         FractionBox["2", "223"]]}
      },
      GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]], ",", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {
        SqrtBox["26"], 
        RowBox[{"18", " ", 
         SqrtBox[
          FractionBox["2", "13"]]}], 
        FractionBox["41", 
         SqrtBox["26"]]},
       {"0", 
        SqrtBox[
         FractionBox["223", "13"]], 
        FractionBox["29", 
         SqrtBox["2899"]]},
       {"0", "0", 
        FractionBox["5", 
         SqrtBox["446"]]}
      },
      GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]]}], "}"}]], "Output",
 CellChangeTimes->{
  3.925098879682623*^9, 3.9250993188961515`*^9, 3.925099427889161*^9, 
   3.9251073756964054`*^9, {3.925107418691803*^9, 3.9251074280846853`*^9}, 
   3.9251075733334427`*^9, 3.925107634871909*^9, {3.9251076889143767`*^9, 
   3.925107738830758*^9}, 3.9251077759632983`*^9, {3.92510781526136*^9, 
   3.925107836598177*^9}, 3.9251082041653175`*^9},
 CellLabel->"Out[43]=",ExpressionUUID->"c0bd8b3a-1571-42b1-853e-65e1b315a5d8"]
}, Open  ]]
}, Open  ]]
},
WindowSize->{935.25, 556.875},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
Magnification:>0.9 Inherited,
FrontEndVersion->"13.1 for Microsoft Windows (64-bit) (2022\:5e746\:670816\
\:65e5)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"a745022f-71b2-45f5-8169-27c3ff4d45e9"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 162, 3, 48, "Subsection",ExpressionUUID->"0af2c2ea-193f-4649-a13d-0c6d54e22272"],
Cell[745, 27, 2390, 57, 315, "Input",ExpressionUUID->"8c29b7ad-df78-4904-86b4-d30b6a44c46b"],
Cell[3138, 86, 800, 17, 26, "Input",ExpressionUUID->"d383ac27-2b85-4a1c-8f34-a880413b2a3f"],
Cell[3941, 105, 1214, 29, 39, "Input",ExpressionUUID->"d5cfeb24-8247-4e06-ac4e-99584add822b"],
Cell[5158, 136, 2279, 54, 170, "Input",ExpressionUUID->"09cbb4b3-a43f-4430-aff6-bc0592dba7aa"],
Cell[7440, 192, 734, 14, 39, "Input",ExpressionUUID->"55d18b28-5e77-464d-841c-e533675bb9e2"],
Cell[8177, 208, 1345, 33, 75, "Input",ExpressionUUID->"cad63f8b-e1a7-4ea9-8cbc-d8ef3fddddb2"],
Cell[9525, 243, 4218, 106, 205, "Input",ExpressionUUID->"05acbbc3-479c-4e50-a4dc-aaf84550f6e8"],
Cell[13746, 351, 5043, 125, 246, "Input",ExpressionUUID->"cf7097dc-67d2-4f27-a92e-0d3cdf2673ba"],
Cell[18792, 478, 754, 14, 39, "Input",ExpressionUUID->"61610133-11de-4935-a818-8eab399e0a08"],
Cell[19549, 494, 1359, 31, 94, "Input",ExpressionUUID->"8330e8f6-05cf-4d38-982e-97240a3d449f"],
Cell[20911, 527, 2272, 54, 170, "Input",ExpressionUUID->"31fd9b80-da51-4399-8d6d-7a7a95dedde9"],
Cell[23186, 583, 2244, 54, 170, "Input",ExpressionUUID->"9427686b-95f7-4bb3-8dd3-6608b56a43f5"],
Cell[25433, 639, 1579, 38, 90, "Input",ExpressionUUID->"80e75e01-3f0c-4715-9e1d-a52d41219a4a"],
Cell[27015, 679, 2491, 61, 170, "Input",ExpressionUUID->"cae67269-c439-4e79-a488-ef1787d38305"],
Cell[29509, 742, 551, 7, 43, "Input",ExpressionUUID->"35a98b0b-7f78-42ba-bedd-e7f6867bf3df"]
}, Open  ]],
Cell[CellGroupData[{
Cell[30097, 754, 148, 3, 48, "Subsection",ExpressionUUID->"8c053a0e-ae75-4d2b-a257-96c36d9e4df0"],
Cell[30248, 759, 5085, 124, 366, "Text",ExpressionUUID->"b16b1ea4-cce2-4a2b-92e1-4cba1822d789"],
Cell[CellGroupData[{
Cell[35358, 887, 870, 17, 39, "Input",ExpressionUUID->"6602253a-4119-44c0-bc64-e5d9454a8813"],
Cell[36231, 906, 2366, 74, 99, "Output",ExpressionUUID->"c0bd8b3a-1571-42b1-853e-65e1b315a5d8"]
}, Open  ]]
}, Open  ]]
}
]
*)