Change search
ReferencesLink to record
Permanent link

Direct link
Convergence factors of Newton methods for nonlinear eigenvalue problems
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).ORCID iD: 0000-0001-9443-8772
2012 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 436, no 10, 3943-3953 p.Article in journal (Refereed) Published
Abstract [en]

Consider a complex sequence convergent to λC with order pN. The convergence factor is typically defined as the fraction ck:=(λk+1-λ)/(λk-λ)p in the limit k. In this paper, we prove formulas characterizing ck in the limit k for two different Newton-type methods for nonlinear eigenvalue problems. The formulas are expressed in terms of the left and right eigenvectors.

The two treated methods are called the method of successive linear problems (MSLP) and augmented Newton and are widely used in the literature. We prove several explicit formulas for ck for both methods. Formulas for both methods are found for simple as well as double eigenvalues. In some cases, we observe in examples that the limit ck as k does not exist. For cases where this limit does not appear to exist, we prove other limiting expressions such that a characterization of ck in the limit is still possible.

Place, publisher, year, edition, pages
Elsevier, 2012. Vol. 436, no 10, 3943-3953 p.
Keyword [en]
Nonlinear eigenvalue problems, Newton’s method, Convergence factors
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-53257DOI: 10.1016/j.laa.2010.08.045ISI: 000303095700010ScopusID: 2-s2.0-84858797047OAI: diva2:469726
Swedish e‐Science Research Center

QC 20141216

Available from: 2011-12-26 Created: 2011-12-26 Last updated: 2014-12-16Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Jarlebring, Elias
By organisation
Numerical Analysis, NA (closed 2012-06-30)
In the same journal
Linear Algebra and its Applications
Computer and Information Science

Search outside of DiVA

GoogleGoogle Scholar
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

Altmetric score

Total: 44 hits
ReferencesLink to record
Permanent link

Direct link