Una extensión del precondicionador I + Smax para el método de Gauss-Seidel

• Arenas, Isnardo ^[1] ; Castillo, Paul ^[1] ; Yong, Xuerong ^[1]
  1. [1] University of Puerto Rico
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 31, Nº. 1, 2013 (Ejemplar dedicado a: Revista Integración), págs. 1-14
• Idioma: español
• Títulos paralelos:
  • An extension of the I + Smax preconditioner for the Gauss-Seidel method
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Se propone una técnica de precondicionamiento para el método deGauss-Seidel basada en la aplicación de una cantidad de pasos arbitrarios perofijos del precondicionador I + Smax. Se analiza de manera teórica la reducción del radio espectral de la matriz de iteración del método de Gauss-Seidel para Z-matrices diagonalmente dominantes. En particular, se demuestra que después de un número finito de pasos esta matriz se reduce a una matriz nula. Para ilustrar la eficacia de la técnica propuesta se presentan experimentos numéricos para una amplia variedad de matrices. Se estudian numéricamente versiones puntuales y de bloques del precondicionador.

  • English

    A preconditioning technique based on the application of a fixedbut arbitrary number of I + Smax steps is proposed. A reduction of the spectral radius of the Gauss-Seidel iteration matrix is theoretically analyzed fordiagonally dominant Z-matrices. In particular, it is shown that after a finitenumber of steps this matrix reduces to null matrix. To illustrate the performance of the proposed technique numerical experiments on a wide variety ofmatrices are presented. Point and block versions of the preconditioner are numerically studied.

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