Mathematics of Computation

Author(s): Tai-Lin Wang; William B. Gragg.
Journal: Math. Comp. 71 (2002), 1473-1496.
MSC (2000): Primary 65F15, 15A18
Posted: November 30, 2001
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Abstract: This paper shows that for unitary Hessenberg matrices the

algorithm, with (an exceptional initial-value modification of) the Wilkinson shift, gives global convergence; moreover, the asymptotic rate of convergence is at least cubic, higher than that which can be shown to be quadratic only for Hermitian tridiagonal matrices, under no further assumption. A general mixed shift strategy with global convergence and cubic rates is also presented.

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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/S0025-5718-01-01387-4
PII: S 0025-5718(01)01387-4
Keywords: $QR$ algorithm, shift strategy, unitary Hessenberg matrices
Received by editor(s): March 9, 1999
Received by editor(s) in revised form: January 6, 2000 and November 7, 2000
Posted: November 30, 2001
Additional Notes: The research of the first author was supported by the Center for Computational Sciences at the University of Kentucky
The research of the second author was supported in part by the National Science Foundation under grant DMS-8704196
Dedicated: Dedicated to the memory of James H. Wilkinson
Copyright of article: Copyright 2001, American Mathematical Society

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