Convergence of the unitary algorithm with a unimodular Wilkinson shift

Authors:
Tai-Lin Wang and William B. Gragg

Journal:
Math. Comp. **72** (2003), 375-385

MSC (2000):
Primary 65F15, 15A18

DOI:
https://doi.org/10.1090/S0025-5718-02-01444-8

Published electronically:
June 25, 2002

MathSciNet review:
1933826

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In applying the algorithm to compute the eigenvalues of a unitary Hessenberg matrix, a *projected* Wilkinson shift of unit modulus is proposed and proved to give global convergence with (at least) a quadratic asymptotic rate for the iteration. Experimental testing demonstrates that the unimodular shift produces more efficient numerical convergence.

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Additional Information

**Tai-Lin Wang**

Affiliation:
Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan, Republic of China

Email:
wang@math.nccu.edu.tw

**William B. Gragg**

Affiliation:
Department of Mathematics, Naval Postgraduate School, Monterey, California 93943

Email:
gragg@nps.navy.mil

DOI:
https://doi.org/10.1090/S0025-5718-02-01444-8

Keywords:
$QR$ algorithm,
shift strategy,
unitary Hessenberg matrices

Received by editor(s):
May 5, 1999

Received by editor(s) in revised form:
April 3, 2001

Published electronically:
June 25, 2002

Additional Notes:
The first author’s research was supported by the Center for Computational Sciences at the University of Kentucky

The second author’s research was supported in part by the National Science Foundation under grant DMS-8704196

Article copyright:
© Copyright 2002
American Mathematical Society