Object
Title: The non-symmetric s-step Lanczos algorithm: Derivation of efficient recurrences and synchronization-reducing variants of BiCG and QMR
Contributor:
Iacono, Mauro - ed. ; Kołodziej, Joanna - ed.
Subtitle:
Group publication title:
Abstract:
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.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
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DOI:
Pages:
Source:
AMCS, volume 25, number 4 (2015) ; click here to follow the link
Language:
Rights:
Biblioteka Uniwersytetu Zielonogórskiego
Object collections:
- Digital Library of Zielona Góra > Repository > Faculties > Faculty of Computer, Electrical and Control Engineering
- Digital Library of Zielona Góra > Repository > Types of work > Articles
- Digital Library of Zielona Góra > Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (2015)
Last modified:
May 6, 2024
In our library since:
May 6, 2024
Number of object content hits:
42
All available object's versions:
https://zbc.uz.zgora.pl/publication/88917
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International Journal of Applied Mathematics and Computer Science (AMCS)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 26 (2016)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 25 (2015)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 25, number 1 (2015)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 25, number 2 (2015)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 25, number 3 (2015)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 25, number 4 (2015)
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