A Cayley-free Two-Step Algorithm for Inverse Singular Value Problems

TL;DR

This paper introduces a novel Cayley-free two-step algorithm for inverse singular value problems, which simplifies computations and achieves cubic root-convergence, validated through numerical experiments.

Contribution

The paper presents a Cayley-free algorithm that avoids Cayley transformations and reduces computational complexity for inverse singular value problems.

Findings

Eliminates Cayley transformations in the algorithm

Achieves cubic root-convergence rate

Validated effectiveness through numerical experiments

Abstract

In this paper, we investigate numerical solutions for inverse singular value problems (for short, ISVPs) arising in various applications. Inspired by the methodologies employed for inverse eigenvalue problems, we propose a Cayley-free two-step algorithm for solving the ISVP. Compared to the existing two-step algorithms for the ISVP, our algorithm eliminates the need for Cayley transformations and consequently avoids solving $2(m+n)$ linear systems during the computation of approximate singular vectors at each outer iteration. Under the assumption that the Jacobian matrix at a solution is nonsingular, we present a convergence analysis for the proposed algorithm and prove a cubic root-convergence rate. Numerical experiments are conducted to validate the effectiveness of our algorithm.