Autor: |
Feuerriegel Stefan, Bücker H. Martin |
Jazyk: |
angličtina |
Rok vydání: |
2015 |
Předmět: |
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Zdroj: |
International Journal of Applied Mathematics and Computer Science, Vol 25, Iss 4, Pp 769-785 (2015) |
Druh dokumentu: |
article |
ISSN: |
2083-8492 |
DOI: |
10.1515/amcs-2015-0055 |
Popis: |
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 synchronization-reducing 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 time-consuming 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. |
Databáze: |
Directory of Open Access Journals |
Externí odkaz: |
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