Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement

This paper presents several new variants of the single-vector Arnoldi algorithm for computing approximations to eigenvalues and eigenvectors of a non-symmetric matrix. The context of this work is the efficient implementation of industrial-strength, parallel, sparse eigensolvers, in which robustness...

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Bibliographic Details
Published in:	Parallel computing Vol. 33; no. 7; pp. 521 - 540
Main Authors:	Hernandez, V., Roman, J.E., Tomas, A.
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.08.2007
Subjects:	Arnoldi eigensolvers Distributed-memory programming Iterative Gram-Schmidt orthogonalization Arnoldi eigensolvers Iterative Gram-Schmidt orthogonalization Distributed-memory programming
ISSN:	0167-8191, 1872-7336
Online Access:	Get full text
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Summary:	This paper presents several new variants of the single-vector Arnoldi algorithm for computing approximations to eigenvalues and eigenvectors of a non-symmetric matrix. The context of this work is the efficient implementation of industrial-strength, parallel, sparse eigensolvers, in which robustness is of paramount importance, as well as efficiency. For this reason, Arnoldi variants that employ Gram-Schmidt with iterative reorthogonalization are considered. The proposed algorithms aim at improving the scalability when running in massively parallel platforms with many processors. The main goal is to reduce the performance penalty induced by global communications required in vector inner products and norms. In the proposed algorithms, this is achieved by reorganizing the stages that involve these operations, particularly the orthogonalization and normalization of vectors, in such a way that several global communications are grouped together while guaranteeing that the numerical stability of the process is maintained. The numerical properties of the new algorithms are assessed by means of a large set of test matrices. Also, scalability analyses show a significant improvement in parallel performance.
ISSN:	0167-8191 1872-7336
DOI:	10.1016/j.parco.2007.04.004