Alternatives for parallel Krylov subspace basis computation

Numerical methods related to Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated via their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for construct...

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Bibliographic Details
Published in:Numerical linear algebra with applications Vol. 4; no. 4; pp. 305 - 331
Main Author: Sidje, Roger B.
Format: Journal Article
Language:English
Published: West Sussex John Wiley & Sons, Ltd 01.07.1997
Subjects:
IBM SP2
Intel Paragon
Krylov subspace
Leja points
parallel QR factorization
sparse matrix
ISSN:1070-5325, 1099-1506
Online Access:Get full text
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Summary:Numerical methods related to Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated via their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. However, although easily parallelizable, this technique is not as scalable as expected for communications. In this work we examine alternative methods aimed at overcoming this drawback. Since they retrieve upon completion the same information as Arnoldi's algorithm does, they enable us to design a wide family of stable and scalable Krylov approximation methods for various parallel environments. We present timing results obtained from their implementation on two distributed‐memory multiprocessor supercomputers: the Intel Paragon and the IBM Scalable POWERparallel SP2. © 1997 John Wiley & Sons, Ltd.
Bibliography:istex:E0DC97C0E777863E83DFDFB006CF9319140A826B
ArticleID:NLA104
ark:/67375/WNG-7RG2L3BD-T
ISSN:1070-5325
1099-1506
DOI:10.1002/(SICI)1099-1506(199707/08)4:4<305::AID-NLA104>3.0.CO;2-D