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Analyzing the convergence factor of residual inverse iteration
Katholieke Univ Leuven, B-3001 Heverlee, Belgium .ORCID iD: 0000-0001-9443-8772
Katholieke Univ Leuven, B-3001 Heverlee, Belgium .
2011 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 51, no 4, 937-957 p.Article in journal (Refereed) Published
Abstract [en]

We will establish here a formula for the convergence factor of the method called residual inverse iteration, which is a method for nonlinear eigenvalue problems and a generalization of the well-known inverse iteration. The formula for the convergence factor is explicit and involves quantities associated with the eigenvalue to which the iteration converges, in particular the eigenvalue and eigenvector. Residual inverse iteration allows for some freedom in the choice of a vector w (k) and we can use the formula for the convergence factor to analyze how it depends on the choice of w (k) . We also use the formula to illustrate the convergence when the shift is close to the eigenvalue. Finally, we explain the slow convergence for double eigenvalues by showing that under generic conditions, the convergence factor is one, unless the eigenvalue is semisimple. If the eigenvalue is semisimple, it turns out that we can expect convergence similar to the simple case.

Place, publisher, year, edition, pages
2011. Vol. 51, no 4, 937-957 p.
Keyword [en]
NONLINEAR EIGENVALUE PROBLEMS; ARNOLDI METHOD; EQUATIONS; SYSTEMS; STATES
National Category
Computer and Information Science
Identifiers
URN: urn:nbn:se:kth:diva-53362DOI: 10.1007/s10543-011-0336-2ISI: 000297362000008OAI: oai:DiVA.org:kth-53362DiVA: diva2:469991
Note
QC 20120207Available from: 2011-12-27 Created: 2011-12-27 Last updated: 2017-12-08Bibliographically approved

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Jarlebring, Elias

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