(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 5101, 160] NotebookOptionsPosition[ 4566, 136] NotebookOutlinePosition[ 4939, 152] CellTagsIndexPosition[ 4896, 149] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ C\[AAcute]lculo Num\[EAcute]rico Enero 2010 \ \>", "Subtitle", CellChangeTimes->{{3.4423192508125*^9, 3.44231925578125*^9}, { 3.471249642328125*^9, 3.471249653984375*^9}}, TextAlignment->Left, TextJustification->0], Cell[CellGroupData[{ Cell["1er Ejercicio", "Section"], Cell[TextData[{ "Dada la matriz A=", Cell[BoxData[ FormBox[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"2", "1", "0", RowBox[{"-", "2"}]}, {"0", "3", "1", RowBox[{"-", "1"}]}, {"0", "0", "3", "1"}, { RowBox[{"-", "1"}], "2", "0", "2"} }, 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$, MatrixForm[BoxForm`e$]]], TraditionalForm]]], " y el vector b=", Cell[BoxData[ FormBox[ SuperscriptBox[ RowBox[{"(", RowBox[{"2", ",", "0", ",", "1", ",", "1"}], ")"}], "t"], TraditionalForm]]], ", se desea resolver el sistema Ax=b mediante el m\[EAcute]todo de Jacobi.\n\ -Obtener la matriz T de jacobi y analizar el radio espectral de la misma para \ determinar si el proceso es convergente.\n-Obtener la soluci\[OAcute]n del \ sistema con un error menor que ", Cell[BoxData[ FormBox[ SuperscriptBox["10", RowBox[{"-", "5"}]], TraditionalForm]], FormatType->"TraditionalForm"], "." }], "Text", CellChangeTimes->{{3.442319301609375*^9, 3.44231932978125*^9}, { 3.442319402375*^9, 3.4423194759375*^9}, {3.4423195286875*^9, 3.442319732484375*^9}, {3.442418520890625*^9, 3.442418521453125*^9}, { 3.471249681328125*^9, 3.4712498025*^9}, {3.4712499201875*^9, 3.471249984953125*^9}, {3.471250032796875*^9, 3.471250178125*^9}, { 3.4712508415*^9, 3.47125093325*^9}, {3.47125096740625*^9, 3.471251016328125*^9}, {3.47254227146875*^9, 3.4725423905625*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["2\.ba Ejercicio", "Section", CellChangeTimes->{{3.4712515675*^9, 3.471251570015625*^9}}], Cell[TextData[{ "Para la siguiente lista de puntos:\ndatos = {{1, -3}, {3, -4.3}, {5, -4.6}, \ {7, -4.7}, {9, -4.8}, {11, -4.8}, {13, -4.85}, {15, -4.85}, {17, -4.9}, {19, \ -4.9}}\na) Obtener, mediante Table, la lista de sus abcisas y de sus \ ordenadas.\nb) Estudiar de las siguientes funciones a cual de ellas se podr\ \[IAcute]a ajustar: \n\n", StyleBox["y=", FontSize->18], Cell[BoxData[ FormBox["a", TraditionalForm]], FontSize->18], "x+b\n", StyleBox["y=", FontSize->18], Cell[BoxData[ FormBox[ FractionBox["1", RowBox[{"ax", "+", "b"}]], TraditionalForm]], FontSize->18], "\n\n", StyleBox["y=", FontSize->18], Cell[BoxData[ FormBox[ RowBox[{ FractionBox["a", "x"], "+", "b"}], TraditionalForm]], FontSize->18], "\n\nc) Analizar el error del ajuste" }], "Text", CellChangeTimes->{{3.442319301609375*^9, 3.44231932978125*^9}, { 3.442319402375*^9, 3.4423194759375*^9}, {3.4423195286875*^9, 3.442319732484375*^9}, {3.442418520890625*^9, 3.442418521453125*^9}, { 3.471249681328125*^9, 3.4712498025*^9}, {3.4712499201875*^9, 3.471249984953125*^9}, {3.471250032796875*^9, 3.471250178125*^9}, { 3.4712508415*^9, 3.47125093325*^9}, {3.47125096740625*^9, 3.471251016328125*^9}, 3.471251955328125*^9, {3.471252792375*^9, 3.471252946890625*^9}, {3.471253017953125*^9, 3.471253107109375*^9}, { 3.4712531371875*^9, 3.47125315390625*^9}, {3.471253383234375*^9, 3.4712534030625*^9}, {3.47125431146875*^9, 3.471254316078125*^9}, { 3.471362817734375*^9, 3.47136282090625*^9}, {3.471363041484375*^9, 3.471363073828125*^9}, {3.471363110296875*^9, 3.471363119890625*^9}}] }, Open ]] }, Open ]] }, WindowToolbars->"EditBar", WindowSize->{943, 758}, WindowMargins->{{-10, Automatic}, {Automatic, 31}}, FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (November 10, 2008)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 252, 6, 49, "Subtitle"], Cell[CellGroupData[{ Cell[844, 32, 32, 0, 71, "Section"], Cell[879, 34, 1882, 50, 115, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[2798, 89, 95, 1, 71, "Section"], Cell[2896, 92, 1642, 40, 237, "Text"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)