Families of Algorithms for Reducing a Matrix to Condensed Form
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Other documents of the author: Van Zee, Field G.; Van de Geijn, Robert A.; Quintana-Ortí, Gregorio; Elizondo, G. Joseph
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Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7036
comunitat-uji-handle3:10234/8620
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http://dx.doi.org/10.1145/2382585.2382587 |
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Title
Families of Algorithms for Reducing a Matrix to Condensed FormDate
2012-11Publisher
ACMBibliographic citation
ACM Transactions on Mathematical Software (TOMS), 39, 1, article 2Type
info:eu-repo/semantics/articlePublisher version
http://dl.acm.org/citation.cfm?id=2382587Subject
Abstract
In a recent paper it was shown how memory traffic can be diminished by reformulating the classic algorithm for reducing a matrix to bidiagonal form, a preprocess when computing the singular values of a dense matrix. ... [+]
In a recent paper it was shown how memory traffic can be diminished by reformulating the classic algorithm for reducing a matrix to bidiagonal form, a preprocess when computing the singular values of a dense matrix. The key is a reordering of the computation so that the most memory-intensive operations can be “fused.” In this article, we show that other operations that reduce matrices to condensed form (reduction to upper Hessenberg form and reduction to tridiagonal form) can be similarly reorganized, yielding different sets of operations that can be fused. By developing the algorithms with a common framework and notation, we facilitate the comparing and contrasting of the different algorithms and opportunities for optimization on sequential architectures. We discuss the algorithms, develop a simple model to estimate the speedup potential from fusing, and showcase performance improvements consistent with the what the model predicts. [-]
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Copyright 2012 ACM
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- ICC_Articles [430]