Mathematics of Computation

Author(s): Tai-Lin Wang; William B. Gragg.
Journal: Math. Comp. 72 (2003), 375-385.
MSC (2000): Primary 65F15, 15A18
Posted: June 25, 2002
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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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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: 10.1090/S0025-5718-02-01444-8
PII: S 0025-5718(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
Posted: 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
Copyright of article: Copyright 2002, American Mathematical Society

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