On an integrable discretization of the Rayleigh quotient gradient system and the power method with a shift

Y. Nakamura, K. Kajiwara, H. Shiotani

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

An integrable discretization of the Rayleigh quotient gradient system is established. The solution of the discrete gradient system is described explicitly and converges exponentially to the same equilibrium point as that of the continuous gradient system for arbitrary large difference step size. It is shown that the discrete gradient system is essentially equivalent to the power method with a shift of origin for calculating the largest eigenvalue. The power method is then proved to be a discrete gradient method.

Original languageEnglish
Pages (from-to)77-90
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume96
Issue number2
DOIs
Publication statusPublished - Sep 15 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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