Abstract

In this review paper, we consider some important developments and trends in algorithm design for the solution of linear systems concentrating on aspects that involve the exploitation of parallelism. We briefly discuss the solution of dense linear systems, before studying the solution of sparse equations by direct and iterative methods. We consider preconditioning techniques for iterative solvers and discuss some of the present research issues in this field. Keywords: linear systems, dense matrices, sparse matrices, tridiagonal systems, parallelism, direct methods, iterative methods, Krylov methods, preconditioning. AMS(MOS) subject classifications: 65F05, 65F50. 1 Introduction Solution methods for systems of linear equations Ax = b; (1) where A is a coefficient matrix of order n and x and b are n-vectors, are usually grouped into two distinct classes: direct methods and iterative methods. However, CCLRC - Rutherford Appleton Laboratory, Oxfordshire, England and CERFACS, Toulouse,...

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