Divide and Conquer the CS Decomposition
Divide and Conquer the CS Decomposition
复制标题
分而治之的CS分解
DOI：
10.1137/120870785
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发表时间：
2013
期刊：
影响因子：
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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
我们开发了一种用于双对角 CS 分解 (CSD) 的分而治之算法。这补充了基于同步 QR 迭代的早期算法。新算法旨在在串行和并行架构上提供熟悉的分而治之算法的效率增益。该解决方案使用了现有算法的许多组件，特别是 Gu 和 Eisenstat 的双对角 SVD 算法，但需要额外的步骤和重新参数化来保持正交性和一致的奇异向量，特别是当奇异向量处于病态时。除了CSD之外，该算法还支持广义奇异值分解（GSVD）的稳定计算。
We develop a divide-and-conquer algorithm for the bidiagonal CS decomposition (CSD). This complements an earlier algorithm based on simultaneous QR iteration. The new algorithm is designed to provide the efficiency gains of familiar divide-and-conquer algorithms on both serial and parallel architectures. The solution uses many components of existing algorithms, particularly the bidiagonal SVD algorithm of Gu and Eisenstat, but extra steps and reparameterizations are required to maintain orthogonality and consistent singular vectors, especially when the singular vectors are ill conditioned. The algorithm supports the stable computation of the generalized singular value decomposition (GSVD) in addition to the CSD.
奇异值分解的双重分治算法的并行性
DOI：
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发表时间：
2007
期刊：
Proceeding of the 25^<th> IASTED International Multi-Conference on Parallel and Distributed Computing and Networks
影响因子：
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作者：
誉田太朗;坪井洋明;高田雅美;岩崎雅史;中村佳正
通讯作者：
中村佳正