The non-symmetric s-step Lanczos algorithm: Derivation of efficient recurrences and synchronization-reducing variants of BICG and QMR

• Autorzy: Stefan Feuerriegel , H. Martin Bücker
• Języki publikacji: EN

Abstrakty

EN

The Lanczos algorithm is among the most frequently used iterative techniques for computing a few dominant eigenvalues of a large sparse non-symmetric matrix. At the same time, it serves as a building block within biconjugate gradient (BiCG) and quasi-minimal residual (QMR) methods for solving large sparse non-symmetric systems of linear equations. It is well known that, when implemented on distributed-memory computers with a huge number of processes, the synchronization time spent on computing dot products increasingly limits the parallel scalability. Therefore, we propose synchronizationreducing variants of the Lanczos, as well as BiCG and QMR methods, in an attempt to mitigate these negative performance effects. These so-called s-step algorithms are based on grouping dot products for joint execution and replacing timeconsuming matrix operations by efficient vector recurrences. The purpose of this paper is to provide a rigorous derivation of the recurrences for the s-step Lanczos algorithm, introduce s-step BiCG and QMR variants, and compare the parallel performance of these new s-step versions with previous algorithms.

Słowa kluczowe

EN

synchronization-reducing; s-step Lanczos; s-step BiCG; s-step QMR; efficient recurrences

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2015
• Tom: 25
• Numer: 4
• Strony: 769-785

Daty

wydano

2015

otrzymano

2014-04-15

poprawiono

2014-10-17

Twórcy

autor

Stefan Feuerriegel

• Chair for Information Systems Research, University of Freiburg, Platz der Alten Synagoge, 79098 Freiburg, Germany

autor

H. Martin Bücker

• Chair for Advanced Computing, Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany

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Identyfikatory

DOI

10.1515/amcs-2015-0055