An error analysis of a unitary Hessenberg QR algorithm

SIAM Journal on Matrix Analysis and Applications

Volumn 28, Issue 1, 2006, Pages 40-67

  Stewart, Michael ^a  

^a GEORGIA STATE UNIVERSITY   (United States)

Author keywords

Unitary eigenvalue problem; Unitary Hessenberg matrix

Indexed keywords

UNITARY EIGENVALUE PROBLEMS; UNITARY HESSENBERG MATRICES;

ERROR ANALYSIS; ITERATIVE METHODS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; SET THEORY;

ALGORITHMS;

EID: 33847118509     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/04061948X     Document Type: Article

References (8)

1. A. BUNSE-GERSTNER AND L. ELSNER, Schur parameter pencils for the solution of the unitary eigenproblem, Linear Algebra Appl., 154/156 (1991), pp. 741-778.
2. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 2nd ed., Johns Hopkins University Press, Baltimore, MD, 1989.
3. W. B. GRAGG, The QR algorithm for unitary Hessenberg matrices, J. Comput. Appl. Math., 16 (1986), pp. 1-8. Cited in [2].
4. W. B. GRAGG, Stabilization of the UHQR algorithm, in Advances in Computational Mathematics, Z. Chen, Y. Li, C. Micchelli, and Y. Xu, eds., Marcel Dekker, New York, 1999, pp. 139-154.
5. N. J. HIGHAM, Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia, 1996.
6. M. STEWART, Stability properties of several variants of the unitary Hessenberg QR algorithm, Contemp. Math. 281, AMS, Providence, RI, 2001.
7. G. SZEGÖ, Orthogonal Polynomials, 3rd ed., AMS, Providence, RI, 1967.
8. T.-L. WANG AND W. B. GRAGG, Convergence of the unitary QR algorithm with a unimodular Wilkinson shift, Math. Comp., 72 (2003), pp. 375-385.