(* 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[     11329,        332]
NotebookOptionsPosition[     11085,        319]
NotebookOutlinePosition[     11427,        334]
CellTagsIndexPosition[     11384,        331]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{
     RowBox[{"sistema", " ", 
      RowBox[{"ejemplo", ":", " ", "\[IndentingNewLine]", 
       RowBox[{"A", ".", "x"}]}]}], "=", "b"}], ",", 
    RowBox[{
     RowBox[{"siendo", " ", "A"}], "=", 
     TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"4", 
          RowBox[{"-", "1"}], "1"},
         {"4", 
          RowBox[{"-", "8"}], "1"},
         {
          RowBox[{"-", "2"}], 
          RowBox[{"-", "1"}], "5"}
        }], "\[NoBreak]", ")"}],
      MatrixForm[#]& ]}], ",", 
    RowBox[{
     RowBox[{"y", " ", "b"}], "=", 
     RowBox[{
      RowBox[{
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"7"},
          {
           RowBox[{"-", "21"}]},
          {"15"}
         }], "\[NoBreak]", ")"}], " ", "x0"}], "=", 
      InterpretationBox[
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"1"},
          {"2"},
          {"2"}
         }], "\[NoBreak]", ")"}],
       MatrixForm[{1, 2, 2}]]}]}]}], "\[IndentingNewLine]", "*)"}], 
  "\[IndentingNewLine]", "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"para", " ", "calcular", " ", "la", " ", "Tg"}], " ", "=", " ", 
    RowBox[{"-", 
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"D", "+", "L"}], ")"}], 
       RowBox[{"-", "1"}]], ".", "U"}]}]}], " ", "*)"}], 
  "\[IndentingNewLine]", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"diag", "=", 
    RowBox[{"DiagonalMatrix", "[", 
     RowBox[{"Diagonal", "[", "A", "]"}], "]"}]}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"L", "=", 
     RowBox[{
      RowBox[{"LowerTriangularize", "[", "A", "]"}], "-", "diag"}]}], ";", 
    RowBox[{"MatrixForm", "[", "L", "]"}]}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"U", "=", 
     RowBox[{
      RowBox[{"UpperTriangularize", "[", "A", "]"}], "-", "diag"}]}], ";", 
    RowBox[{"MatrixForm", "[", "U", "]"}]}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"Tg", "=", 
     RowBox[{"-", 
      RowBox[{
       RowBox[{"Inverse", "[", 
        RowBox[{"diag", "+", "L"}], "]"}], ".", "U"}]}]}], ";", 
    RowBox[{"MatrixForm", "[", "Tg", "]"}]}], "\[IndentingNewLine]", 
   RowBox[{"Max", "[", 
    RowBox[{"Abs", "[", 
     RowBox[{"Eigenvalues", "[", "Tg", "]"}], "]"}], "]"}], 
   "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", 
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{"Bucle", " ", "para", " ", "Gauss"}], "-", 
     RowBox[{"Seidel", 
      RowBox[{"(", " ", 
       RowBox[{
        RowBox[{"k", " ", "y", " ", "k"}], "+", "1"}], ")"}]}]}], " ", "*)"}],
    "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"a", "=", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"4.", ",", 
         RowBox[{"-", "1."}], ",", "1."}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"4.", ",", 
         RowBox[{"-", "8."}], ",", "1."}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"-", "2."}], ",", 
         RowBox[{"-", "1."}], ",", "5."}], "}"}]}], "}"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"b", "=", 
     RowBox[{"{", 
      RowBox[{"7.", ",", 
       RowBox[{"-", "21."}], ",", "15."}], "}"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"n", "=", 
     RowBox[{"Length", "[", "b", "]"}]}], ";"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{"aproximacion", " ", "inicial"}], ",", " ", 
     RowBox[{"y", " ", "usando", " ", "while", " ", "con", " ", "la", " ", 
      RowBox[{"tolerancia", ":"}]}]}], " ", "*)"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"xant", "=", 
     RowBox[{"{", 
      RowBox[{"0.", ",", "0", ",", "0"}], "}"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"xnuev", "=", "xant"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"error", "=", "1"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"tol", "=", 
     RowBox[{"10", "^", 
      RowBox[{"(", 
       RowBox[{"-", "4"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"k", "=", "0"}], ";"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{"(*", " ", 
    RowBox[{"bucle", " ", "principal", " ", "while"}], " ", "*)"}], 
   "\[IndentingNewLine]", 
   RowBox[{"While", "[", 
    RowBox[{
     RowBox[{"error", "\[GreaterEqual]", "tol"}], ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"k", "=", 
       RowBox[{"k", "+", "1"}]}], ";", "\[IndentingNewLine]", 
      RowBox[{"Do", "[", "\[IndentingNewLine]", "\t", 
       RowBox[{
        RowBox[{
         RowBox[{"xnuev", "[", 
          RowBox[{"[", "i", "]"}], "]"}], "=", 
         RowBox[{
          FractionBox["1", 
           RowBox[{"a", "[", 
            RowBox[{"[", 
             RowBox[{"i", ",", "i"}], "]"}], "]"}]], "*", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"b", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "-", 
            RowBox[{
             UnderoverscriptBox["\[Sum]", 
              RowBox[{"j", "=", "1"}], 
              RowBox[{"i", "-", "1"}]], 
             RowBox[{
              RowBox[{"a", "[", 
               RowBox[{"[", 
                RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", 
              RowBox[{"xnuev", "[", 
               RowBox[{"[", "j", "]"}], "]"}]}]}], "-", 
            RowBox[{
             UnderoverscriptBox["\[Sum]", 
              RowBox[{"j", "=", 
               RowBox[{"i", "+", "1"}]}], "n"], 
             RowBox[{
              RowBox[{"a", "[", 
               RowBox[{"[", 
                RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", 
              RowBox[{"xant", "[", 
               RowBox[{"[", "j", "]"}], "]"}]}]}]}], ")"}]}]}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "1", ",", "n"}], "}"}]}], "]"}], ";", 
      "\[IndentingNewLine]", "   ", 
      RowBox[{"Print", "[", 
       RowBox[{"\"\<Iteracion: \>\"", ",", "k"}], "]"}], ";", 
      "\[IndentingNewLine]", "   ", 
      RowBox[{"Print", "[", 
       RowBox[{"\"\<Nueva aproximaci\[OAcute]n: \>\"", ",", "xnuev"}], "]"}], 
      ";", "\[IndentingNewLine]", "   ", 
      RowBox[{"error", "=", 
       RowBox[{
        RowBox[{"Norm", "[", 
         RowBox[{
          RowBox[{"xnuev", "-", "xant"}], ",", "\[Infinity]"}], "]"}], "/", 
        RowBox[{"Norm", "[", 
         RowBox[{"xnuev", ",", "\[Infinity]"}], "]"}]}]}], " ", ";", 
      "\[IndentingNewLine]", "   ", 
      RowBox[{"Print", "[", 
       RowBox[{"\"\<Error relativo: \>\"", ",", "error"}], "]"}], ";", 
      "\[IndentingNewLine]", 
      RowBox[{"xant", "=", "xnuev"}]}]}], "]"}], "\[IndentingNewLine]", 
   "\[IndentingNewLine]", 
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{
     "si", " ", "ponemos", " ", "el", " ", "numero", " ", "de", " ", 
      "iteraciones", " ", "K"}], ",", " ", 
     RowBox[{"con", " ", "dos", " ", "Do", " ", "anidados"}]}], " ", "*)"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"A", "=", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"4.", ",", 
         RowBox[{"-", "1."}], ",", "1."}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{"4.", ",", 
         RowBox[{"-", "8."}], ",", "1."}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"-", "2."}], ",", 
         RowBox[{"-", "1."}], ",", "5."}], "}"}]}], "}"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"b", "=", 
     RowBox[{"{", 
      RowBox[{"7", ",", 
       RowBox[{"-", "21"}], ",", "15"}], "}"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"n", "=", 
     RowBox[{"Length", "[", "b", "]"}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"xant", "=", 
     RowBox[{"{", 
      RowBox[{"1.", ",", "2.", ",", "2."}], "}"}]}], ";"}], 
   "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"xnuev", "=", "xant"}], ";"}], "\[IndentingNewLine]", 
   RowBox[{"(*", " ", 
    RowBox[{"bucle", " ", "principal", " ", "Do", " ", "anidados"}], " ", 
    "*)"}], "\[IndentingNewLine]", 
   RowBox[{"Do", "[", "\[IndentingNewLine]", "\t", 
    RowBox[{
     RowBox[{
      RowBox[{"Do", "[", 
       RowBox[{
        RowBox[{
         RowBox[{"xnuev", "[", 
          RowBox[{"[", "i", "]"}], "]"}], "=", 
         RowBox[{
          FractionBox["1", 
           RowBox[{"A", "[", 
            RowBox[{"[", 
             RowBox[{"i", ",", "i"}], "]"}], "]"}]], "*", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"b", "[", 
             RowBox[{"[", "i", "]"}], "]"}], "-", 
            RowBox[{
             UnderoverscriptBox["\[Sum]", 
              RowBox[{"j", "=", "1"}], 
              RowBox[{"i", "-", "1"}]], 
             RowBox[{
              RowBox[{"A", "[", 
               RowBox[{"[", 
                RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", 
              RowBox[{"xnuev", "[", 
               RowBox[{"[", "j", "]"}], "]"}]}]}], "-", 
            RowBox[{
             UnderoverscriptBox["\[Sum]", 
              RowBox[{"j", "=", 
               RowBox[{"i", "+", "1"}]}], "n"], 
             RowBox[{
              RowBox[{"A", "[", 
               RowBox[{"[", 
                RowBox[{"i", ",", "j"}], "]"}], "]"}], "*", 
              RowBox[{"xant", "[", 
               RowBox[{"[", "j", "]"}], "]"}]}]}]}], ")"}]}]}], ",", 
        RowBox[{"{", 
         RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ";", "\[IndentingNewLine]", 
      "\t  ", 
      RowBox[{"Print", "[", "xnuev", "]"}], ";", "\[IndentingNewLine]", 
      "           ", 
      RowBox[{"erabs", "=", 
       RowBox[{"Norm", "[", 
        RowBox[{
         RowBox[{"xnuev", "-", "xant"}], ",", "\[Infinity]"}], "]"}]}], ";", 
      "\[IndentingNewLine]", "           ", 
      RowBox[{"errel", "=", 
       RowBox[{"erabs", "/", 
        RowBox[{"Norm", "[", 
         RowBox[{"xnuev", ",", "\[Infinity]"}], "]"}]}]}], ";", "  ", 
      "\[IndentingNewLine]", "           ", 
      RowBox[{"Print", "[", 
       RowBox[{"\"\<Error absoluto: \>\"", ",", "erabs"}], "]"}], ";", 
      "\[IndentingNewLine]", "           ", 
      RowBox[{"Print", "[", 
       RowBox[{"\"\<Error relativo: \>\"", ",", "errel"}], "]"}], ";", 
      "\[IndentingNewLine]", "\t   ", 
      RowBox[{"xant", "=", "xnuev"}]}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"k", ",", "1", ",", "5"}], "}"}]}], "]"}]}]}]], "Input",
 CellChangeTimes->{{3.6560984504312983`*^9, 3.656098505547509*^9}, {
  3.6560987006781044`*^9, 3.6560987440550575`*^9}}]
},
WindowSize->{716, 537},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"9.0 for Microsoft Windows (32-bit) (January 25, 2013)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 10524, 297, 1357, "Input"]
}
]
*)

(* End of internal cache information *)