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Volume 41, Issue 6
Implicit Determinant Method for Solving an Hermitian Eigenvalue Optimization Problem

Siru Gong & Yangfeng Su

DOI: 10.4208/jcm.2203-m2020-0303

J. Comp. Math., 41 (2023), pp. 1117-1136.

Published online: 2023-11

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  • Abstract

Implicit determinant method is an effective method for some linear eigenvalue optimization problems since it solves linear systems of equations rather than eigenpairs. In this paper, we generalize the implicit determinant method to solve an Hermitian eigenvalue optimization problem for smooth case and non-smooth case. We prove that the implicit determinant method converges locally and quadratically. Numerical experiments confirm our theoretical results and illustrate the efficiency of implicit determinant method.

  • Keywords

Eigenvalue optimization, Multiple eigenvalue, Non-smooth optimization, Implicit determinant method, Crawford number.

  • AMS Subject Headings

15A18, 65F15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-41-1117, author = {Gong , Siru and Su , Yangfeng}, title = {Implicit Determinant Method for Solving an Hermitian Eigenvalue Optimization Problem}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {41}, number = {6}, pages = {1117--1136}, abstract = {

Implicit determinant method is an effective method for some linear eigenvalue optimization problems since it solves linear systems of equations rather than eigenpairs. In this paper, we generalize the implicit determinant method to solve an Hermitian eigenvalue optimization problem for smooth case and non-smooth case. We prove that the implicit determinant method converges locally and quadratically. Numerical experiments confirm our theoretical results and illustrate the efficiency of implicit determinant method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2203-m2020-0303}, url = {http://global-sci.org/intro/article_detail/jcm/22106.html} }
TY - JOUR T1 - Implicit Determinant Method for Solving an Hermitian Eigenvalue Optimization Problem AU - Gong , Siru AU - Su , Yangfeng JO - Journal of Computational Mathematics VL - 6 SP - 1117 EP - 1136 PY - 2023 DA - 2023/11 SN - 41 DO - http://doi.org/10.4208/jcm.2203-m2020-0303 UR - https://global-sci.org/intro/article_detail/jcm/22106.html KW - Eigenvalue optimization, Multiple eigenvalue, Non-smooth optimization, Implicit determinant method, Crawford number. AB -

Implicit determinant method is an effective method for some linear eigenvalue optimization problems since it solves linear systems of equations rather than eigenpairs. In this paper, we generalize the implicit determinant method to solve an Hermitian eigenvalue optimization problem for smooth case and non-smooth case. We prove that the implicit determinant method converges locally and quadratically. Numerical experiments confirm our theoretical results and illustrate the efficiency of implicit determinant method.

Gong , Siru and Su , Yangfeng. (2023). Implicit Determinant Method for Solving an Hermitian Eigenvalue Optimization Problem. Journal of Computational Mathematics. 41 (6). 1117-1136. doi:10.4208/jcm.2203-m2020-0303
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