A new algorithm for singular value decomposition and its parallelization

Authors:
Taro Konda;Yoshimasa Nakamura
Affiliations:
Graduate School of Informatics, Department of Applied Mathematics and Physics, Kyoto University, Yoshidahonnmachi, Sakyo-ku, Kyoto 606-8501, Japan;Graduate School of Informatics, Department of Applied Mathematics and Physics, Kyoto University, Yoshidahonnmachi, Sakyo-ku, Kyoto 606-8501, Japan and SORST, Japan Science and Technology Agency, J ...
Venue:
Parallel Computing
Year:
2009

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Abstract

An algorithm mainly consisting of a part of Divide and Conquer and the twisted factorization is proposed for bidiagonal SVD. The algorithm costs O(n^2)flops and is highly parallelizable when singular values are isolated. If strong clusters exist, the singular vector computation needs reorthgonalization. In such case, the cost of the algorithm increases to O(n^2+nk^2)flops and the parallelism may worsen depending on the distribution of singular values. Here k is the size of the largest cluster. The algorithm needs only O(n) working memory for every type of matrices.