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Disguised and new quasi-Newton methods for nonlinear eigenvalue problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0001-9443-8772
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2017 (English)In: Numerical Algorithms, ISSN 1017-1398, E-ISSN 1572-9265Article in journal (Refereed) In press
Abstract [en]

In this paper, we take a quasi-Newton approach to nonlinear eigenvalue problems (NEPs) of the type M(λ)v = 0, where (Formula presented.) is a holomorphic function. We investigate which types of approximations of the Jacobian matrix lead to competitive algorithms, and provide convergence theory. The convergence analysis is based on theory for quasi-Newton methods and Keldysh’s theorem for NEPs. We derive new algorithms and also show that several well-established methods for NEPs can be interpreted as quasi-Newton methods, and thereby, we provide insight to their convergence behavior. In particular, we establish quasi-Newton interpretations of Neumaier’s residual inverse iteration and Ruhe’s method of successive linear problems.

Place, publisher, year, edition, pages
Springer, 2017.
Keyword [en]
Inverse iteration, Iterative methods, Nonlinear eigenvalue problems, Quasi-Newton methods
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-218702DOI: 10.1007/s11075-017-0438-2Scopus ID: 2-s2.0-85034666004OAI: oai:DiVA.org:kth-218702DiVA, id: diva2:1161440
Note

QC 20171211

Available from: 2017-11-30 Created: 2017-11-30 Last updated: 2018-02-15Bibliographically approved

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Jarlebring, EliasKoskela, AnttiMele, Giampaolo
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