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Volume 9, Issue 4
An Ulm-Like Cayley Transform Method for Inverse Eigenvalue Problems with Multiple Eigenvalues

Weiping Shen, Chong Li & Xiaoqing Jin

DOI: 10.4208/nmtma.2016.y15030

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 664-685.

Published online: 2016-09

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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.

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@Article{NMTMA-9-664, author = {Weiping Shen, Chong Li and Xiaoqing Jin}, title = {An Ulm-Like Cayley Transform Method for Inverse Eigenvalue Problems with Multiple Eigenvalues}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {4}, pages = {664--685}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2016.y15030}, url = {http://global-sci.org/intro/article_detail/nmtma/12394.html} }
TY - JOUR T1 - An Ulm-Like Cayley Transform Method for Inverse Eigenvalue Problems with Multiple Eigenvalues AU - Weiping Shen, Chong Li & Xiaoqing Jin JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 664 EP - 685 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2016.y15030 UR - https://global-sci.org/intro/article_detail/nmtma/12394.html KW - AB -

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.

Weiping Shen, Chong Li and Xiaoqing Jin. (2016). An Ulm-Like Cayley Transform Method for Inverse Eigenvalue Problems with Multiple Eigenvalues. Numerical Mathematics: Theory, Methods and Applications. 9 (4). 664-685. doi:10.4208/nmtma.2016.y15030
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