A quadratically convergent algorithm for inverse singular value problems with multiple singular values

Abstract

In 2021, for inverse singular value problems, a quadratically convergent algorithm (Wei and Chen, 2021) based on matrix multiplication (Ogita and Aishima, 2020) was designed for inverse singular value problems. Although this method has some good features compared to other quadratic convergence methods, it is not suitable for multiple singular values. In this paper, we propose a modified algorithm adapted to an arbitrary set of given singular values. Moreover, under some mild assumptions, we prove its quadratic convergence in the root sense. Numerical experiments show that the effectiveness and practicality of the proposed method.