循环约简算法的一种并行和矢量变体

Siam Journal on Scientific and Statistical Computing Pub Date : 1988-07-01 DOI:10.1137/0909050

R. Sweet

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引用次数: 77

摘要

块循环约简算法的Buneman变体开始时是一个高度并行的算法，但随着每次约简而崩溃为一个非常串行的算法。利用有理矩阵函数的部分分式展开，说明了如何恢复并行性。使用$n^2 $处理器的结果算法在$O(\log ^2 n)$时间内运行。

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A Parallel and Vector Variant of the Cyclic Reduction Algorithm

The Buneman variant of the block cyclic reduction algorithm begins as a highly parallel algorithm, but collapses with each reduction to a very serial one. Using partial fraction expansions of rational matrix functions, it is shown how to regain the parallelism. The resulting algorithm using $n^2 $ processors runs in $O(\log ^2 n)$ time.

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Siam Journal on Scientific and Statistical Computing

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