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A parallel implementation of the CMRH method for dense linear systems

✍ Scribed by Sébastien Duminil

Book ID
120755075
Publisher
Springer US
Year
2012
Tongue
English
Weight
923 KB
Volume
63
Category
Article
ISSN
1017-1398

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✦ Synopsis

This paper presents an implementation of the CMRH (Changing Minimal Residual method based on the Hessenberg process) iterative method suitable for parallel architectures. CMRH is an alternative to GMRES and QMR, the well-known Krylov methods for solving linear systems with nonsymmetric coefficient matrices. CMRH generates a (non orthogonal) basis of the Krylov subspace through the Hessenberg process. On dense matrices, it requires less storage than GMRES. Parallel numerical experiments on a distributed memory computer with up to 16 processors are shown on some applications related to the solution of dense linear systems of equations. A comparison with the GMRES method is also provided on those test examples.

Keywords

Linear systems • Krylov method • Hessenberg process • Dense matrix • Parallel implementation • MPI • CMRH • GMRES • Preconditioned CMRH

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