Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • 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
  • rtf
BROYDEN'S METHOD FOR NONLINEAR EIGENPROBLEMS
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, Centres, SeRC - Swedish e-Science Research Centre.ORCID iD: 0000-0001-9443-8772
2019 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 41, no 2, p. A989-A1012Article in journal (Refereed) Published
Abstract [en]

Broyden's method is a general method commonly used for nonlinear systems of equations when very little information is available about the problem. We develop an approach based on Broyden's method for the structure appearing in nonlinear eigenvalue problems. Our approach is designed for problems where the evaluation of a matrix vector product is computationally expensive, essentially as expensive as solving the corresponding linear system of equations. We show how the structure of the Jacobian matrix can be incorporated into the algorithm to improve convergence. The algorithm exhibits local superlinear convergence for simple eigenvalues, and we characterize the convergence. We show how deflation can be integrated and combined such that the method can be used to compute several eigenvalues. A specific problem in machine tool milling, coupled with a PDE, is used to illustrate the approach. The simulations were carried out using the Julia programming language, and the simulation software is provided publicly for reproducibility.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS , 2019. Vol. 41, no 2, p. A989-A1012
Keywords [en]
nonlinear eigenproblems, Broyden methods, Newton methods, time-delay systems, eigenvalue problems, CKER DW, 1985, SIAM JOURNAL ON NUMERICAL ANALYSIS, V22, P566 zanson Jeff, 2017, SIAM REVIEW, V59, P65 oyden C.G., 1973, Journal of the Institute of Mathematics and Its Applications, V12, P223 rrett C. Kristopher, 2016, ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, V43, UFLHARD P., 2004, Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, yld Daniel B., 2015, NUMERISCHE MATHEMATIK, V129, P383
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-254045DOI: 10.1137/18M1173150ISI: 000469225300013Scopus ID: 2-s2.0-85065566542OAI: oai:DiVA.org:kth-254045DiVA, id: diva2:1342275
Note

QC 20190813

Available from: 2019-08-13 Created: 2019-08-13 Last updated: 2019-08-13Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Jarlebring, Elias

Search in DiVA

By author/editor
Jarlebring, Elias
By organisation
Mathematics (Dept.)SeRC - Swedish e-Science Research Centre
In the same journal
SIAM Journal on Scientific Computing
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 1 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • 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
  • rtf