Block Gauss elimination followed by a classical iterative method for the solution of linear systems

Authors:
Maria Alanelli;Apostolos Hadjidimos
Affiliations:
Department of Mathematics, University of Crete, GR-714 09 Heraklion, Greece;Department of Mathematics, University of Crete, GR-714 09 Heraklion, Greece
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

In the last two decades many papers have appeared in which the application of an iterative method for the solution of a linear system is preceded by a step of the Gauss elimination process in the hope that this will increase the rates of convergence of the iterative method. This combination of methods has been proven successful especially when the matrix A of the system is an M-matrix. The purpose of this paper is to extend the idea of one to more Gauss elimination steps, consider other classes of matrices A, e.g., p-cyclic consistently ordered, and generalize and improve the asymptotic convergence rates of some of the methods known so far.