Geodesic
Fast and stable unitary QR algorithm
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 327-341
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.
Classification : 65F15, 65H17, 15A18, 15B10
Keywords: eigenvalue, unitary matrix, francis's QR algorithm, core transformations rotators 
@article{ETNA_2015__44__a13,
     author = {Aurentz,  Jared L. and Mach,  Thomas and Vandebril,  Raf and Watkins,  David S.},
     title = {Fast and stable unitary {QR} algorithm},
     journal = {Electronic transactions on numerical analysis},
     pages = {327--341},
     year = {2015},
     volume = {44},
     zbl = {1327.65071},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a13/}
}
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AU  - Watkins,  David S.
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%A Vandebril,  Raf
%A Watkins,  David S.
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%J Electronic transactions on numerical analysis
%D 2015
%P 327-341
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%G en
%F ETNA_2015__44__a13
Aurentz,  Jared L.; Mach,  Thomas; Vandebril,  Raf; Watkins,  David S. Fast and stable unitary QR algorithm. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 327-341. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a13/