An inexact Ulm-type method based on matrix multiplication for inverse singular value problems
Wei Ma
School of Mathematics and Statistics, Nanyang Normal University, Nanyang, Henan, People's Republic of China
Keywords: inverse singular value problems, inverse eigenvalue problems, Ulm-type method, Newton's method, Cayley transform, quadratically convergent
Abstract
Based on the idea of Ogita and Aishima [1] and Ulm's method [2], we designed an inexact Ulm-type method based on matrix multiplication for inverse singular value problems, which avoids the shortcomings of solving a system of linear equations in each iteration of the algorithm in [3]. Thus, it looks more stable and requires less computations. Under the condition that the given singular values are distinct, the algorithm has the quadratic convergence in the sense of root convergence. Moreover, numerical experiments in the last section show that the new method is better than some known algorithms.
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