Modified and Generalized GMRES Iterative Algorithmsof Lanczos-Type
by
David Kincaid
University of Texas at Austin
Coauthors: Jen-Yuan Chen (I-Shou University, Taiwan), David M. Young (University of Texas at Austin)

We are interested in iterative methods for solving systems of linear equations of the form Au=b, where A is a large sparse nonsingular matrix. When A is symmetric positive definite, conjugate-gradient-type methods are often used and are fairly well understood. On the other hand, when A is nonsymmetric, the choice of iterative method is much more difficult.

We consider the GGMRES method, which is a slight generalization of the GMRES method, as well as two other methods-MGMRES and LAN/MGMRES. Instead of using a minimization process as in GGMRES, we use a Galerkin condition to derive the MGMRES method. The LAN/MGMRES method is designed to combine the reliability of GMRES with the reduced work of a Lanczos-type method.

A computer program has been implemented based on the use of the LAN/MGMRES algorithm for solving nonsymmetric linear systems arising from certain elliptic problems. Numerical tests have been carried out comparing this algorithm with some other iterative algorithms.

Modified and Generalized GMRES Iterative Algorithmsof Lanczos-Type

Date received: February 6, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caen-05.