Fast and stable unitary QR algorithm
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Date
2015
Authors
Aurentz, Jared L.
Mach, Thomas
Vandebril, Raf
Watkins, David S.
Journal Title
Journal ISSN
Volume Title
Publisher
Electronic Transactions on Numerical Analysis
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.
Description
Keywords
core transformations rotators, eigenvalue, Francis's QR algorithm, unitary matrix
Citation
Aurentz, J. L., Mach, T., Vandebril, R., & Watkins, D. S. (2015). Fast and stable unitary QR algorithm. Electronic Transactions on Numerical Analysis, 44, 327-341.