On the local convergence of an iterative approach for inverse singular value problems |
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| Authors: | Zheng-Jian Bai Benedetta Morini Shu-fang Xu |
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| Institution: | 1. Department of Mathematics, Chinese University of Hong Kong, Shatin, NT, Hong Kong, PR China;2. Dipartimento di Energetica ‘S. Stecco’ Università di Firenze, Via C. Lombroso 6/17, 50134 Firenze, Italy;3. School of Mathematical Sciences, Peking University, Beijing 100871, PR China |
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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. |
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| Keywords: | Inverse problems Singular values Root-convergence rate Newton method |
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