Parallel iterative S-step methods for unsymmetric linear systems

GCR (Generalized Conjugate Residual) and Omin (Orthomin) are iterative methods for approximating the solution of unsymmetric linear systems. The S-step generalization of these methods has been derived and studied in past work. The S-step methods exhibit improved convergence properties. Also, their d...

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Bibliographic Details
Published in:Parallel computing 1996, Vol.22 (5), p.623-641
Main Authors: Chronopoulos, A.T., Swanson, C.D.
Format: Article
Language:English
Subjects:
Cray C90
Iterative methods
Modified Gram-Schmidt
S-step Orthomin
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Summary:GCR (Generalized Conjugate Residual) and Omin (Orthomin) are iterative methods for approximating the solution of unsymmetric linear systems. The S-step generalization of these methods has been derived and studied in past work. The S-step methods exhibit improved convergence properties. Also, their data locality and parallel properties are enhanced by forming blocks of s search direction vectors. However, s is limited (to s ≤ 5) by numerical stability considerations. The following new contributions are described in this article. The Modified Gram-Schmidt method is used to A T A-orthogonalize the s direction vectors within each S-step block. It is empirically shown that use of values of s, up to s = 16, preserves the numerical stability of the new iterative methods. Finally, the new S-step Omin, implemented on the CRAY C90, attained an execution rate greater than 10 Gflops (Billion Floating Point Operations per sec).
ISSN:0167-8191
1872-7336
DOI:10.1016/0167-8191(96)00022-1