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El primero es una combinacion de las \ matrices triangular inferior y superior, el segundo es un vector que \ especifica las filas que se han usado en el pivoteo, y el tercero es una \ estimaci\[OAcute]n del n\.ba de condici\[OAcute]n de la matriz. El comando \ LUMatrices[ ] transforma el resultado de la matriz conjunta que devuelve el \ comando LUDecomposition, en dos matrices L y U, de modo que ya se puede \ realizar el proceso de resolucion del sistema en dos etapas. Se debe tener en \ cuenta que si el comando LUDecomposition ha realizado intercambio de filas, \ tambien se debera aplicar dicho intercambio a el vector b , termino \ independiente del sistema que se pretende resolver." }], "Subsection", TextAlignment->Left, TextJustification->1] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Ejercicio 2\.ba", FontVariations->{"Underline"->True}], "\nResolver el siguiente sistema usando la factorizaci\[OAcute]n de \ Choleski:\n6", Cell[BoxData[ FormBox[ SubscriptBox["x", "1"], TraditionalForm]]], "+2", Cell[BoxData[ FormBox[ SubscriptBox["x", "2"], TraditionalForm]]], "+", Cell[BoxData[ FormBox[ SubscriptBox["x", "3"], TraditionalForm]]], "-", Cell[BoxData[ FormBox[ SubscriptBox["x", "4"], TraditionalForm]]], "=0\n2", Cell[BoxData[ FormBox[ SubscriptBox["x", "1"], TraditionalForm]]], "+4", Cell[BoxData[ FormBox[ SubscriptBox["x", "2"], TraditionalForm]]], "+", Cell[BoxData[ FormBox[ SubscriptBox["x", "3"], TraditionalForm]]], " =7\n", Cell[BoxData[ FormBox[ SubscriptBox["x", "1"], TraditionalForm]]], "+", Cell[BoxData[ FormBox[ SubscriptBox["x", "2"], TraditionalForm]]], "+4", Cell[BoxData[ FormBox[ SubscriptBox["x", "3"], TraditionalForm]]], "-", Cell[BoxData[ FormBox[ SubscriptBox["x", "4"], TraditionalForm]]], " =-1\n-", Cell[BoxData[ FormBox[ SubscriptBox["x", "1"], TraditionalForm]]], "-", Cell[BoxData[ FormBox[ SubscriptBox["x", "3"], TraditionalForm]]], "+3", Cell[BoxData[ FormBox[ SubscriptBox["x", "4"], TraditionalForm]]], " =-2" }], "Section"], Cell["\<\ La descomposici\[OAcute]n de Cholesky se aplica a una matriz \ sim\[EAcute]trica definida positiva y da como resultado el producto de una \ matriz triangular superior por una triangular inferior que es la traspuesta \ de la anterior. \ \>", "Subsection", CellChangeTimes->{3.5075623317760305`*^9}, TextAlignment->Left, TextJustification->1] }, Open ]] }, Open ]] }, WindowToolbars->{"RulerBar", "EditBar"}, WindowSize->{1028, 746}, WindowMargins->{{3, Automatic}, {Automatic, 30}}, CellLabelAutoDelete->True, FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (February 18, 2009)", StyleDefinitions->FrontEnd`FileName[{"Report"}, "StandardReport.nb", CharacterEncoding -> "WindowsANSI"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 85, 2, 81, "Title"], Cell[CellGroupData[{ Cell[677, 28, 2019, 55, 401, "Section"], Cell[2699, 85, 108, 1, 24, "Subsection"], Cell[2810, 88, 670, 13, 127, "Subsection"], Cell[CellGroupData[{ Cell[3505, 105, 451, 8, 75, "Subsection"], Cell[3959, 115, 8546, 220, 456, "Input"], Cell[12508, 337, 9003, 236, 792, "Input"] }, Open ]], Cell[21526, 576, 1018, 17, 127, "Subsection"] }, Open ]], Cell[CellGroupData[{ Cell[22581, 598, 1321, 61, 203, "Section"], Cell[23905, 661, 355, 8, 41, "Subsection"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)