A Jacobi-Davidson type method for the two-parameter eigenvalue problem

M.E. Hochstenbach, T. Kosir, Bor Plestenjak

    Research output: Contribution to journalArticleAcademicpeer-review

    30 Citations (Scopus)

    Abstract

    We present a new numerical method for computing selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. The method does not require good initial approximations and is able to tackle large problems that are too expensive for methods that compute all eigenvalues. The new method uses a two-sided approach and is a generalization of the Jacobi--Davidson type method for right definite two-parameter eigenvalue problems [M. E. Hochstenbach and B. Plestenjak, SIAM J. Matrix Anal. Appl., 24 (2002), pp. 392--410]. Here we consider the much wider class of nonsingular problems. In each step we first compute Petrov triples of a small projected two-parameter eigenvalue problem and then expand the left and right search spaces using approximate solutions to appropriate correction equations. Using a selection technique, it is possible to compute more than one eigenpair. Some numerical examples are presented.
    Original languageEnglish
    Pages (from-to)477-497
    JournalSIAM Journal on Matrix Analysis and Applications
    Volume26
    Issue number2
    DOIs
    Publication statusPublished - 2005

    Fingerprint

    Dive into the research topics of 'A Jacobi-Davidson type method for the two-parameter eigenvalue problem'. Together they form a unique fingerprint.

    Cite this