Volume 44, pp. 327-341, 2015.

Fast and stable unitary QR algorithm

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

Abstract

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.

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Key words

eigenvalue, unitary matrix, Francis's QR algorithm, core transformations rotators

AMS subject classifications

65F15, 65H17, 15A18, 15B10

Links to the cited ETNA articles

[35]Vol. 40 (2013), pp. 17-35 Raf Vandebril and David S. Watkins: An extension of the QZ algorithm beyond the Hessenberg-upper triangular pencil

ETNA articles which cite this article

Vol. 46 (2017), pp. 447-459 Jared L. Aurentz, Thomas Mach, Raf Vandebril, and David S. Watkins: Computing the eigenvalues of symmetric tridiagonal matrices via a Cayley transformation

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