Iterative refinement for singular value decomposition based on matrix multiplication

Abstract

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.