Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 32 No. 1 (2014): Revista Integración, temas de matemáticas
Research and Innovation Articles

An acceleration technique for the Gauss-Seidel method applied to symmetric linear systems

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  • Jesús Cajigas,
  • Isnardo Arenas,
  • Paul Castillo
Jesús Cajigas
University of Puerto Rico
Bio
Isnardo Arenas
The University of Texas at Dallas
Paul Castillo
University of Puerto Rico

Published 2014-05-22

Keywords

  • Preconditioning,
  • Gauss-Seidel method,
  • regular splitting.

How to Cite

Cajigas, J., Arenas, I., & Castillo, P. (2014). An acceleration technique for the Gauss-Seidel method applied to symmetric linear systems. Revista Integración, Temas De matemáticas, 32(1), 91–100. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4065

Abstract

A preconditioning technique to improve the convergence of the Gauss-Seidel method applied to symmetric linear systems while preserving symmetry is proposed. The preconditioner is of the form I + K and can be applied an arbitrary number of times. It is shown that under certain conditions the application of the preconditioner a finite number of steps reduces the matrix to a diagonal. A series of numerical experiments using matrices from spatial discretizations of partial differential equations demonstrates that both versions of the preconditioner, point and block version, exhibit lower iteration counts than its non-symmetric version.

To cite this article: J. Cajigas, I. Arenas, P. Castillo, An acceleration technique for the Gauss-Seidel method applied to symmetric linear systems, Rev. Integr. Temas Mat. 32 (2014), no. 1, 91–100.

 

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