Necessary and sufficient conditions for convergence of the QR algorithm on Hessenberg matrix

  • Authors:

  • Beresford Parlett

  • Affiliations:

  • -

  • Venue:
  • ACM '66 Proceedings of the 1966 21st national conference
  • Year:
  • 1966

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Abstract

The QR Algorithm was developed1 to find the eigen - values of real or complex matrices. We shall consider it here in the context of exact arithmetic. Sufficient conditions for convergence, listed in order of increasing strength, have been given.1,2,3,7 It seems that necessary and sufficient conditions would be very complicated for a general matrix.