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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 5, Pages 787–799
DOI: https://doi.org/10.31857/S0044466921050094 (Mi zvmmf11238) 		 
This article is cited in 2 scientific papers (total in 2 papers)

General numerical methods

New algorithms for solving nonlinear eigenvalue problems

W. Ganderab

a 8092 Zurich, Ramistrasse 1010, ETH, Switzerland
b Hong Kong Baptist University, 224 Waterloo Rd, Kowloon Tong, Hong Kong
Citations (2)
DOI: https://doi.org/10.31857/S0044466921050094
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.
Key words: nonlinear eigenvalue problem, third order methods, algorithmic differentiation.
Received: 24.12.2020
Revised: 24.12.2020
Accepted: 14.01.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 5, Pages 761–773
DOI: https://doi.org/10.1134/S0965542521050092
Bibliographic databases:
Document Type: Article
UDC: 519.614
Language: Russian
Citation: W. Gander, “New algorithms for solving nonlinear eigenvalue problems”, Zh. Vychisl. Mat. Mat. Fiz., 61:5 (2021), 787–799; Comput. Math. Math. Phys., 61:5 (2021), 761–773
Citation in format AMSBIB
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\paper New algorithms for solving nonlinear eigenvalue problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\issue 5
\pages 787--799
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\crossref{https://doi.org/10.31857/S0044466921050094}
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\transl
\jour Comput. Math. Math. Phys.
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  • https://www.mathnet.ru/eng/zvmmf/v61/i5/p787
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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