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New Algorithms for Solving Nonlinear Eigenvalue Problems

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Abstract

To solve a nonlinear eigenvalue problem we develop algorithms which compute zeros of \(\det A(\lambda ) = 0\). We show how to apply third order iteration methods for that purpose. The necessary derivatives of the determinant are computed by algorithmic differentiation. Since many nonlinear eigenvalue problems have banded matrices we also present an algorithm which makes use of their structure.

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Notes

  1. http://www.maths.manchester.ac.uk/our-research/research-groups/numerical-analysis-and-scientific-computing/numerical-analysis/software/nlevp/

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ACKNOWLEDGMENTS

The author would like to thank Zhong-Zhi Bai and Yu-Mei Huang, the two organizers of the 2019 Golub Memorial Workshop in Lanzhou. The invitation to participate at this conference was a special motivation for me to develop the algorithms discussed in this paper.

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Authors and Affiliations

  1. ETH, 8092, Zurich, Switzerland

    W. Gander

  2. Hong Kong Baptist University, Kowloon Tong, Hong Kong

    W. Gander

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  1. W. Gander
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Correspondence to W. Gander.

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Gander, W. New Algorithms for Solving Nonlinear Eigenvalue Problems. Comput. Math. and Math. Phys. 61, 761–773 (2021). https://doi.org/10.1134/S0965542521050092

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  • DOI: https://doi.org/10.1134/S0965542521050092

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