Iterative refinement for singular value decomposition based on matrix multiplication

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:369

Article

Ogita, Takeshi¹  Aishima, Kensuke² 

[1] Tokyo Womans Christian Univ, Sch Arts & Sci, Tokyo, Japan

[2] Hosei Univ, Fac Comp & Informat Sci, Tokyo, Japan

关键词: SVD;    Iterative refinement;    Convergence analysis;    Higher-precision arithmetic;   

DOI  :  10.1016/j.cam.2019.112512

来源: Elsevier

【 摘 要 】

We propose a refinement algorithm for singular value decomposition (SVD) of a real matrix. In the same manner as Newton's method, the proposed algorithm converges quadratically if a modestly accurate initial guess is given. Since the proposed algorithm is based on matrix multiplication, it can efficiently be implemented. Numerical results demonstrate the excellent performance of the proposed algorithm in terms of the convergence rate and the measured computing time compared to a standard approach using multiple precision arithmetic. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free