BIT Numerical Mathematics

, Volume 36, Issue 3, pp 494–508

On conjugate gradient-like methods for eigen-like problems

  • Alan Edelman
  • Steven T. Smith

DOI: 10.1007/BF01731929

Cite this article as:
Edelman, A. & Smith, S.T. Bit Numer Math (1996) 36: 494. doi:10.1007/BF01731929


Numerical analysts, physicists, and signal processing engineers have proposed algorithms that might be called conjugate gradient for problems associated with the computation of eigenvalues. There are many variations, mostly one eigenvalue at a time though sometimes block algorithms are proposed. Is there a correct “conjugate gradient” algorithm for the eigenvalue problem? How are the algorithms related amongst themselves and with other related algorithms such as Lanczos, the Newton method, and the Rayleigh quotient?

Key words

Conjugate gradientLanczosNewton's Methodoptimizationsignal processingelectronic structuresdifferential geometry

Copyright information

© BIT Foundation 1996

Authors and Affiliations

  • Alan Edelman
    • 1
  • Steven T. Smith
    • 2
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Lincoln LaboratoryMassachusetts Institute of TechnologyLexingtonUSA