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The infinite Lanczos method for symmetric nonlinear eigenvalue problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, Centres, SeRC - Swedish e-Science Research Centre.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

A new iterative method for solving large scale symmetric nonlineareigenvalue problems is presented. We firstly derive an infinite dimensional symmetric linearization of the nonlinear eigenvalue problem, then we apply the indefinite Lanczos method to this specific linearization, resulting in a short-term recurrence. We show how, under specific assumption on the starting vector, this method can be carried out in finite arithmetic and how the exploitation of the problem structure leads to improvements in terms of computation time. The eigenpair approximations are extracted with the nonlinear Rayleigh–Ritz procedure combined with aspecific choice of the projection space. We illustrate how this extraction technique resolves the instability issues that may occur due to the loss of orthogonality in many standard Lanczos-type methods.

Keywords [en]
nonlinear eigenvalue problem, symmetric, Lanczos
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics, Numerical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-263723OAI: oai:DiVA.org:kth-263723DiVA, id: diva2:1369213
Funder
Swedish Research Council, 621-2013-4640
Note

QCR 20191111

Available from: 2019-11-11 Created: 2019-11-11 Last updated: 2019-11-11Bibliographically approved

Open Access in DiVA

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arXiv:1812.07557

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Mele, Giampaolo
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Numerical Analysis, NASeRC - Swedish e-Science Research Centre
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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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