Fast and stable unitary QR algorithm

Jared L. Aurentz, Thomas Mach, Raf Vandebril, David S. Watkins

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


A fast Fortran implementation of a variant of Gragg's unitary Hessenberg QR algorithm is presented. It is proved, moreover, that all QR- And QZ-like algorithms for the unitary eigenvalue problems are equivalent. The algorithm is backward stable. Numerical experiments are presented that confirm the backward stability and compare the speed and accuracy of this algorithm with other methods.

Original languageEnglish
Pages (from-to)327-341
Number of pages15
JournalElectronic Transactions on Numerical Analysis
Publication statusPublished - 2015
Externally publishedYes


  • Core transformations rotators
  • Eigenvalue
  • Francis's QR algorithm
  • Unitary matrix

ASJC Scopus subject areas

  • Analysis

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