Performance of a new scheme for bidiagonal singular value decomposition of large scale

Authors:
Masami Takata;Kinji Kimura;Masashi Iwasaki;Yoshimasa Nakamura
Affiliations:
PRESTO, JST, Graduate School of Informatics, Kyoto University, Kyoto, JAPAN;CREST, JST, College of Science, Rikkyo University, Tokyo, JAPAN;PRESTO, JST, Graduate School of Informatics, Kyoto University, Kyoto, JAPAN;PRESTO, JST, Graduate School of Informatics, Kyoto University, Kyoto, JAPAN
Venue:
PDCN'06 Proceedings of the 24th IASTED international conference on Parallel and distributed computing and networks
Year:
2006

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Abstract

To perform singular value decomposition (SVD) of matrices with high accuracy and high-speed, we developed a library by using an integrable system called the discrete Lotka-Volterra (dLV) system. The most well-known routine for the SVD is DBDSQR provided in LAPACK, which is based on the QRs (QR with shift) algorithm. However, DBDSQR is slow and does not perform well for the case where only a few singular vectors are desirable. Recently a new SVD scheme named Integrable-SVD (I-SVD) was developed. The execution time for the I-SVD scheme based on the dLV system and transformation is less. In this paper, we implement and evaluate the I-SVD scheme. To examine its accuracy, we propose a method for making random upper bidiagonal matrices with desired singular values. The corresponding singular vectors are also accurately obtained. From the experimental results, we conclude that the singular vectors computed by the I-SVD scheme have adequate orthogonality, and the scheme also has high speed and accuracy for both the computed singular values and vectors.