Block quasi-minimal residual iterations for non-Hermitian linear systems
- AT&T Bell Labs., Murray Hill, NJ (United States)
Many applications require the solution of multiple linear systems that have the same coefficient matrix, but differ only in their right-hand sides. Instead of applying an iterative method to each of these systems individually, it is usually more efficient to employ a block version of the method that generates blocks of iterates for all the systems simultaneously. An example of such an iteration is the block conjugate gradient algorithm, which was first studied by Underwood and O`Leary. On parallel architectures, block versions of conjugate gradient-type methods are attractive even for the solution of single linear systems, since they have fewer synchronization points than the standard versions of these algorithms. In this talk, the author presents a block version of Freund and Nachtigal`s quasi-minimal residual (QMR) method for the iterative solution of non-Hermitian linear systems. He describes two different implementations of the block-QMR method, one based on a block version of the three-term Lanczos algorithm and one based on coupled two-term block recurrences. In both cases, the underlying block-Lanczos process still allows arbitrary normalizations of the vectors within each block, and the author discusses different normalization strategies. To maintain linear independence within each block, it is usually necessary to reduce the block size in the course of the iteration, and the author describes a deflation technique for performing this reduction. He also present some convergence results, and reports results of numerical experiments with the block-QMR method. Finally, the author discusses possible block versions of transpose-free Lanczos-based iterations such as the TFQMR method.
- Research Organization:
- Front Range Scientific Computations, Inc., Boulder, CO (United States); US Department of Energy (USDOE), Washington DC (United States); National Science Foundation, Washington, DC (United States)
- OSTI ID:
- 219555
- Report Number(s):
- CONF-9404305-Vol.2; ON: DE96005736; TRN: 96:002321-0002
- Resource Relation:
- Conference: Colorado conference on iterative methods, Breckenridge, CO (United States), 5-9 Apr 1994; Other Information: PBD: [1994]; Related Information: Is Part Of Colorado Conference on iterative methods. Volume 2; PB: 261 p.
- Country of Publication:
- United States
- Language:
- English
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