Newton-type methods for inverse singular value problems with multiple singular values

We consider the convergence problem of some Newton-type methods for solving the inverse singular value problem with multiple and positive singular values. Under the nonsingularity assumption of the relative generalized Jacobian matrices at the solution c⁎c⁎, a convergence analysis for the multiple and positive case is provided and the superlinear or quadratical convergence properties are proved. Moreover, numerical experiments are given in the last section and comparisons are made.