Families of Algorithms for Reducing a Matrix to Condensed Form
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http://dx.doi.org/10.1145/2382585.2382587 |
Metadades
Títol
Families of Algorithms for Reducing a Matrix to Condensed FormData de publicació
2012-11Editor
ACMCita bibliogràfica
ACM Transactions on Mathematical Software (TOMS), 39, 1, article 2Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
http://dl.acm.org/citation.cfm?id=2382587Paraules clau / Matèries
Resum
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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