• Medientyp: E-Artikel
  • Titel: General Rayleigh Quotient Iteration
  • Beteiligte: Geltner, Peter B.
  • Erschienen: Society for Industrial and Applied Mathematics, 1981
  • Erschienen in: SIAM Journal on Numerical Analysis, 18 (1981) 5, Seite 839-843
  • Sprache: Englisch
  • ISSN: 0036-1429
  • Entstehung:
  • Anmerkungen:
  • Beschreibung: The Rayleigh quotient is generalized to the form <tex-math>$\rho_c = \langle Ax, Bx \rangle_C/\|Bx\|^2_C$</tex-math>, where C is a Hermitian, positive definite matrix. General Rayleigh quotient iteration is applied to the problem Ax = λ Bx, and under certain conditions quadratic local convergence is proved. An example is given in which it is shown that Rayleigh quotient iteration diverges in a neighborhood of an eigenvector, while Blum-Rodrigue quotient iteration converges.