A refined Arnoldi type method for large scale eigenvalue problems

Xiang Wang*, Qiang Niu, Lin Zhang Lu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


We present a refined Arnoldi-type method for extracting partial eigenpairs of large matrices. The approximate eigenvalues are the Ritz values of (A-τ I)-1 with respect to a shifted Krylov subspace. The approximate eigenvectors are derived by satisfying certain optimal properties, and they can be computed cheaply by a small sized singular value problem. Theoretical analysis show that the approximate eigenpairs computed by the new method converges as the approximate subspace expands. Finally, numerical results are reported to show the efficiency of the new method.

Original languageEnglish
Pages (from-to)129-143
Number of pages15
JournalJapan Journal of Industrial and Applied Mathematics
Issue number1
Publication statusPublished - Feb 2013


  • Arnoldiprocess
  • Eigenvalue problem
  • Harmonic Ritz values
  • Rayleigh-Ritz
  • Ritz values

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