Convergence of the Newton-type methods for the square inverse singular value problems with multiple and zero singular values

Abstract

In this paper, we study the convergence of the Newton-type methods for solving the square inverse singular value problem with possible multiple and zero singular values. Comparing with other known results, positivity assumption of the given singular values is removed. Under the nonsingularity assumption in terms of the (relative) generalized Jacobian matrices, quadratic/superlinear convergence properties (in the root-convergence sense) are proved. Moreover, numerical experiments are given to demonstrate our theoretic results.