Families of Algorithms for Reducing a Matrix to Condensed Form
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http://dx.doi.org/10.1145/2382585.2382587 |
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Título
Families of Algorithms for Reducing a Matrix to Condensed FormFecha de publicación
2012-11Editor
ACMCita bibliográfica
ACM Transactions on Mathematical Software (TOMS), 39, 1, article 2Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://dl.acm.org/citation.cfm?id=2382587Palabras clave / Materias
Resumen
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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