Stable Computation of the CS Decomposition: Simultaneous Bidiagonalization
Stable Computation of the CS Decomposition: Simultaneous Bidiagonalization
复制标题
CS 分解的稳定计算：同时双对角化
DOI：
10.1137/100813002
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Brian D. Sutton
中科院分区：
文献类型：
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作者：
Brian D. Sutton
自1977年发现以来，CS分解（CSD）一直抵制计算，即使它是众所周知的特征值和奇异值分解的兄弟。几个算法已经开发了减少2-1形式的分解，但没有被扩展到完整的2-2形式的分解在斯图尔特的原始文件。在这篇文章中，我们提出了一个算法，同时双对角化的四个块的酉矩阵划分成一个2 × 2块结构。这是CSD两阶段算法的第一个直接阶段，就像Golub-Kahan-Reinsch双对角化是计算奇异值分解的第一阶段一样。证明了后向稳定性。
Since its discovery in 1977, the CS decomposition (CSD) has resisted computation, even though it is a sibling of the well-understood eigenvalue and singular value decompositions. Several algorithms have been developed for the reduced 2-by-1 form of the decomposition, but none have been extended to the complete 2-by-2 form of the decomposition in Stewart's original paper. In this article, we present an algorithm for simultaneously bidiagonalizing the four blocks of a unitary matrix partitioned into a 2-by-2 block structure. This serves as the first, direct phase of a two-stage algorithm for the CSD, much as Golub-Kahan-Reinsch bidiagonalization serves as the first stage in computing the singular value decomposition. Backward stability is proved.
DOI：
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发表时间：
2007
期刊：
Lecture Notes in Computer Science(Springer-Verlag) 4671
影响因子：
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作者：
Yamamoto;Y.;Fukaya;T.;Uneyama;T.;Takata;M.;Kimura;K.;Iwasaki;M;Nakamura;Y
通讯作者：
Y