Synchronization-reducing variants of the Biconjugate Gradient and the quasi-Minimal Residual Methods

Open access
Date
2013Type
- Conference Paper
ETH Bibliography
no
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Abstract
The Biconjugate Gradient (BiCG) and the Quasi-Minimal Residual (QMR) method are among the popular iterative methods for the solution of large, sparse, non-symmetric systems of linear equations. When these methods are implemented on large-scale parallel computers, their scalability is limited by the synchronization caused when carrying out inner product-like operations. Therefore, we propose two new synchronization-reducing variants of BiCG and QMR in an attempt to mitigate these negative performance effects. The idea behind these new s-step variants is to group several dot products for joint execution. Although these new algorithms still reveal numerical instabilities, they are shown to keep the cost of inner product-like operations almost independent of the number of processes, thus improving scalability significantly. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000182414Publication status
publishedExternal links
Book title
Algorithms and Architectures for Parallel ProcessingJournal / series
Lecture Notes in Computer ScienceVolume
Pages / Article No.
Publisher
SpringerEvent
Subject
s-step BiCG; s-step QMR; synchronization-reducingOrganisational unit
09623 - Feuerriegel, Stefan (ehemalig) / Feuerriegel, Stefan (former)
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ETH Bibliography
no
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