Acceleration of iterative refinement for singular value decomposition

Yuki Uchino, Takeshi Terao, Katsuhisa Ozaki

研究成果: Article査読

抄録

We propose fast numerical algorithms to improve the accuracy of singular vectors for a real matrix. Recently, Ogita and Aishima proposed an iterative refinement algorithm for singular value decomposition that is constructed with highly accurate matrix multiplications carried out six times per iteration. The algorithm runs for the problem that has no multiple and clustered singular values. In this study, we show that the same algorithm can be run with highly accurate matrix multiplications carried out five times. Also, we proposed four algorithms constructed with highly accurate matrix multiplications, two algorithms with the multiplications carried out four times, and the other two with the multiplications carried out five times. These algorithms adopt the idea of a mixed-precision iterative refinement method for linear systems. Numerical experiments demonstrate speed-up and quadratic convergence of the proposed algorithms. As a result, the fastest algorithm is 1.7 and 1.4 times faster than the Ogita-Aishima algorithm per iteration on a CPU and GPU, respectively.

本文言語English
ページ(範囲)979-1009
ページ数31
ジャーナルNumerical Algorithms
95
2
DOI
出版ステータスPublished - 2024 2月

ASJC Scopus subject areas

  • 応用数学

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