(07) Sol de Sistemas de Ecuaciones Parte 2

(07) Sol de Sistemas de Ecuaciones Parte 2 - Sistemas de...

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Sistemas de Sistemas de Ecuaciones Solución de Sistemas de Ecuaciones Lineales (Parte 2) Descomposición LU Ing. Armandina J. Leal Flores
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Solución de Sistemas de Ecuaciones Álgebra Matricial • Matrices y Vectores • Operaciones con Matrices y Vectores • Determinante • Inversa Sistemas de Ecuaciones Lineales •Método Gráfico • Regla de Cramer • Eliminación de Gauss • Descomposición LU • Gauss-Seidel Sistemas de Ecuaciones No Lineales • Newton Raphson
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Solución del Sistema de Ecuaciones Primer paso de eliminación de Gauss
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Ventajas… ¡ Disminuye la cantidad de operaciones para resolver un sistema de ecuaciones. ¡ Es mucho más sencillo de programar. ¡ Es más eficiente para resolver sistemas con los mismos coeficientes (A) pero distintas constantes (b)
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Descomposición LU Ejemplo A = 3 2 1 11 7 5 19 17 13 ! " # # # $ % & & & B = 0 0 1 ! " # # # $ % & & & 3 x + 2 y + z = 0 11 x + 7 y + 5 z = 0 19 x + 17 y + 13 z = 1 3 2 1 11 7 5 19 17 13 ! " # # # $ % & & & ------> 3 2 1 11 3 1 3 4 3 19 3 13 3 20 3 ! " # # # # # $ % & & & & & ------> 3 2 1 11 3 1 3 4 3 19 3 13 24 ! " # # # # # $ % & & & & & 3 2 1 0 1 3 4 3 0 13 3 20 3 " # $
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