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Name:

Miloslav Znojil

Reviewer number:

9689

Email:

Item's zbl-Number:

DE 018 027 247

Author(s):

Wang, Tai-Lin; Gragg, William B.:

Shorttitle:

Convergence of the shifted QR algorithm for unitary hessenberg matrices

Source:

Math. Comput. 71, No. 240, 1473 - 1496 (2002).

Classification:

Primary Classification:

65F15

Eigenvalues, eigenvectors

Secondary Classification:

15A18

Eigenvalues, singular values, and eigenvectors

Keywords:

QR algorithm; shift strategy; unitary Hessenberg matrices

Review:

There are differences between Hessenberg matrices, at least from the
point of view of the QR algorithm. The authors argue that in contrast
to the generic case (where the asymptotic rate of convergence may be
shown quadratic, for the tridiagonal case at lest), an additional
requirement of the unitarity of the matrix may play a crucial role.
They prove that under this assumption the rate of the convergence
becomes at least cubic. Moreover, a recommended (modified) Wilkinson
shift is able to lead to the convergence which is global. In a climax
of the story a mixed strategy is analyzed and recommended. Based on
the PhD thesis of the first author.

Remarks to the editors:

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