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An Ulm-like Cayley Transform Method for Inverse Eigenvalue Problems with Multiple Eigenvalues

Part of: Numerical linear algebra

Published online by Cambridge University Press:  17 November 2016

Weiping Shen ,
Chong Li  and
Xiaoqing Jin
Weiping Shen*
Affiliation:
Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China
Chong Li*
Affiliation:
School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China
Xiaoqing Jin*
Affiliation:
Department of Mathematics, University of Macau, Macao, China
*
*Corresponding author. Email addresses:shenweiping@zjnu.cn (W.-P. Shen), cli@zju.edu.cn (C. Li), xqjin@umac.mo (X.-Q. Jin)
*Corresponding author. Email addresses:shenweiping@zjnu.cn (W.-P. Shen), cli@zju.edu.cn (C. Li), xqjin@umac.mo (X.-Q. Jin)
*Corresponding author. Email addresses:shenweiping@zjnu.cn (W.-P. Shen), cli@zju.edu.cn (C. Li), xqjin@umac.mo (X.-Q. Jin)
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Abstract

We study the convergence of an Ulm-like Cayley transform method for solving inverse eigenvalue problems which avoids solving approximate Jacobian equations. Under the nonsingularity assumption of the relative generalized Jacobian matrices at the solution, a convergence analysis covering both the distinct and multiple eigenvalues cases is provided and the quadratical convergence is proved. Moreover, numerical experiments are given in the last section to illustrate our results.

Keywords

Nonlinear equationinverse eigenvalue problemUlm-like method

MSC classification

Secondary: 65F18: Inverse eigenvalue problems 65F10: Iterative methods for linear systems 65F15: Eigenvalues, eigenvectors
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 4 , November 2016 , pp. 664 - 685
Copyright
Copyright © Global-Science Press 2016 

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