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Solving Linear Equations on Parallel Distributed Memory Architectures By Extrapolation
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BibTeX
@MISC{Andersson_solvinglinear,
author = {Christer Andersson},
title = {Solving Linear Equations on Parallel Distributed Memory Architectures By Extrapolation},
year = {}
}
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Abstract
Extrapolation methods can be used to accelerate the convergence of vector sequences. It is shown how three different extrapolation algorithms, the minimal polynomial extrapolation (MPE), the reduced rank extrapolation (RRE) and the modified minimal polynomial extrapolation (MMPE), can be used to solve systems of linear equations. The algorithms are derived and equivalence to different Krylov subspace methods are established. The extrapolation algorithms are to prefer on parallel distributed memory architectures since less inter-processor communication is needed. Numerically the extrapolation methods are not as stable as the Krylov subspace methods since they require the solution of ill-conditioned overdetermined systems. Several techniques of improving convergence and stability are presented. Some of these are new to the best of the author's knowledge. The use of regularization methods and a slightly modified stationary method have proved to be especially useful. Error bounds and metho...
Keyphrases
parallel distributed memory architecture linear equation extrapolation method minimal polynomial extrapolation several technique different extrapolation algorithm extrapolation algorithm vector sequence reduced rank extrapolation regularization method ill-conditioned overdetermined system stationary method inter-processor communication different krylov subspace method krylov subspace method
