Volume 59, pp. 60-88, 2023.
The bisection eigenvalue method for unitary Hessenberg matrices via their quasiseparable structure
Yuli Eidelman and Iulian Haimovici
Abstract
If
We describe here a fast procedure, which takes only
The performance of the developed
algorithm is illustrated by a series of numerical tests. The algorithm is more accurate and many times faster
(when executed in Matlab) than for
general Hermitian matrices of quasiseparable order two, because the action of the quasiseparable generators,
which are small matrices in the previous cited paper, can be replaced by scalars, most of them real numbers.
Full Text (PDF) [426 KB], BibTeX , DOI: 10.1553/etna_vol59s60
Key words
quasiseparable, eigenstructure, Sturm property, bisection, unitary Hessenberg
AMS subject classifications
15A18, 15B10, 15B57, 65F15
Links to the cited ETNA articles
[8] | Vol. 44 (2015), pp. 342-366 Yuli Eidelman and Iulian Haimovici: The fast bisection eigenvalue method for Hermitian order one quasiseparable matrices and computations of norms |
[19] | Vol. 58 (2023), pp. 316-347 Yuli Eidelman and Iulian Haimovici: Improved bisection eigenvalue method for band symmetric Toeplitz matrices |