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The Homotopy Method for the Complete Solution of Quadratic Two-parameter Eigenvalue Problems

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Abstract

We propose a homotopy method to solve the quadratic two-parameter eigenvalue problems, which arise frequently in the analysis of the asymptotic stability of the delay differential equation. Our method does not require to form coupled generalized eigenvalue problems with Kronecker product type coefficient matrices and thus can avoid the increasing of the computational cost and memory storage. Numerical results and the applications in the delay differential equations are presented to illustrate the effectiveness and efficiency of our method. It appears that our method tends to be more effective than the existing methods in terms of speed, accuracy and memory storage as the problem size grows.

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Acknowledgements

The author would like to thank the editor and anonymous referees for their careful reading and valuable comments and suggestions that significantly improve the presentation of this article.

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  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, Liaoning, China

    Bo Dong

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This work was supported in part by the National Natural Science Foundation of China (Grant No. 11871136) and the Fundamental Research Funds for the Central Universities.

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Dong, B. The Homotopy Method for the Complete Solution of Quadratic Two-parameter Eigenvalue Problems. J Sci Comput 90, 18 (2022). https://doi.org/10.1007/s10915-021-01693-8

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