On the local convergence of an iterative approach for inverse singular value problems

Authors:
Zheng-Jian Bai;Benedetta Morini;Shu-fang Xu
Affiliations:
Department of Information and Computational Mathematics, Xiamen University, Xiamen, People's Republic of China and Department of Mathematics, Chinese University of Hong Kong, Hong Kong, PR China;Dipartimento di Energetica 'S. Stecco' Università di Firenze, Firenze, Italy;School of Mathematical Sciences, Peking University, Beijing, PR China
Venue:
Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
Year:
2007

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Abstract

The purpose of this paper is to provide the convergence theory for the iterative approach given by M.T. Chu [Numerical methods for inverse singular value problems, SIAM J. Numer. Anal. 29 (1992), pp. 885-903] in the context of solving inverse singular value problems. We provide a detailed convergence analysis and show that the ultimate rate of convergence is quadratic in the root sense. Numerical results which confirm our theory are presented. It is still an open issue to prove that the method is Q-quadratic convergent as claimed by M.T. Chu.