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.
On the Local Convergence of an Iterative Approach for Inverse Singular Value Problems / BAI Z.-J; B. MORINI; XU S.F. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - STAMPA. - 198:(2007), pp. 344-360. [10.1016/j.cam.2005.06.050]
On the Local Convergence of an Iterative Approach for Inverse Singular Value Problems
MORINI, BENEDETTA;
2007
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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