Rayleigh-Ritz and Lanczos methods for symmetric matrix pencils

Peter Lancaster, Qiang Ye

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We are concerned with eigenvalue problems for definite and indefinite symmetric matrix pencils. First, Rayleigh-Ritz methods are formulated and, using Krylov subspaces, a convergence analysis is presented for definite pencils. Second, generalized symmetric Lanczos algorithms are introduced as a special Rayleigh-Ritz method. In particular, an a posteriori convergence criterion is demonstrated by using residuals. Local convergence to real and nonreal eigenvalues is also discussed. Numerical examples concerning vibrations of damped cantilever beams are included.

Original languageEnglish
Pages (from-to)173-201
Number of pages29
JournalLinear Algebra and Its Applications
Issue numberC
StatePublished - May 1993

Bibliographical note

Funding Information:
in part by the National

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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