Change search
CiteExportLink to record
Permanent link

Direct link
Cite
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
  • rtf
Pseudospectra and Linearization Techniques of Rational Eigenvalue Problems
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2013 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

This thesis concerns the analysis and sensitivity of nonlinear eigenvalue problems for matrices and linear operators. The first part illustrates that lack of normality may result in catastrophic ill-conditioned eigenvalue problem. Linearization of rational eigenvalue problems for both operators over finite and infinite dimensional spaces are considered. The standard approach is to multiply by the least common denominator in the rational term and apply a well known linearization technique to the polynomial eigenvalue problem. However, the symmetry of the original problem is lost, which may result in a more ill-conditioned problem. In this thesis, an alternative linearization method is used and the sensitivity of the two different linearizations are studied. Moreover, this work contains numerically solved rational eigenvalue problems with applications in photonic crystals. For these examples the pseudospectra is used to show how well-conditioned the problems are which indicates whether the solutions are reliable or not.

Place, publisher, year, edition, pages
2013. , 93 p.
Keyword [en]
Pseudospectra, Linearization, Rational Eigenvalue Problems
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-79466OAI: oai:DiVA.org:umu-79466DiVA: diva2:641889
Presentation
(Swedish)
Available from: 2013-10-23 Created: 2013-08-19 Last updated: 2013-10-23Bibliographically approved

Open Access in DiVA

fulltext(878 kB)287 downloads
File information
File name FULLTEXT01.pdfFile size 878 kBChecksum SHA-512
f569c2662741deb631b5733d486e13f7c72c5488c019e7b0ec7303875b10191c619213a43c7bef6ecec75303db904613268dffb0901057d8d46baa49b475eff5
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Torshage, Axel
By organisation
Department of Mathematics and Mathematical Statistics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 287 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 292 hits
CiteExportLink to record
Permanent link

Direct link
Cite
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
  • rtf