A backward error for the inverse singular value problem

Abstract: A backward error for inverse singular value problems with respect to an approximate solution is defined, and an explicit expression for the backward error is derived by extending the approach described in [J.G. Sun, Backward errors for the inverse eigenvalue problem, Numer. Math. 82 (1999) 339–349]. The expression may be useful for testing the stability of practical algorithms. [Copyright &y& Elsevier]