Volume 3, pp. 160-176, 1995.

A parallel GMRES version for general sparse matrices

Jocelyne Erhel


This paper describes the implementation of a parallel variant of GMRES on Paragon. This variant builds an orthonormal Krylov basis in two steps: it first computes a Newton basis then orthogonalises it. The first step requires matrix-vector products with a general sparse unsymmetric matrix and the second step is a QR factorisation of a rectangular matrix with few long vectors. The algorithm has been implemented for a distributed memory parallel computer. The distributed sparse matrix-vector product avoids global communications thanks to the initial setup of the communication pattern. The QR factorisation is distributed by using Givens rotations which require only local communications. Results on an Intel Paragon show the efficiency and the scalability of our algorithm.

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Key words

GMRES, parallelism, sparse matrix, Newton basis.

AMS subject classifications

65F10, 65F25, 65F50.

ETNA articles which cite this article

Vol. 40 (2013), pp. 381-406 Desire Nuentsa Wakam and Jocelyne Erhel: Parallelism and robustness in GMRES with a Newton basis and deflated restarting
Vol. 47 (2017), pp. 206-230 David Imberti and Jocelyne Erhel: Varying the s in your s-step GMRES

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