Convergence of a Ulm-like method for square inverse singular value problems with multiple and zero singular values

Abstract

An interesting problem was raised in Vong et al. (SIAM J. Matrix Anal. Appl. 32:412–429, 2011): whether the Ulm-like method and its convergence result can be extended to the cases of multiple and zero singular values. In this paper, we study the convergence of a Ulm-like method for solving the square inverse singular value problem with multiple and zero singular values. Under the nonsingularity assumption in terms of the relative generalized Jacobian matrices, a convergence analysis for the multiple and zero case is provided and the quadratical convergence property is proved. Moreover, numerical experiments are given in the last section to demonstrate our theoretic results.