The unitary completion and QR iterations for a class of structured matrices

Mathematics of Computation

Volumn 77, Issue 261, 2008, Pages 353-378

  Bini, D A ^a   Eidelman, Y ^b   Gemignani, L ^a   Gohberg, I ^b  

^a UNIVERSITY OF PISA   (Italy)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Companion matrices; Complexity; Eigenvalue computation; Hessenberg matrices; QR iteration; Quasiseparable matrices; Rank one perturbations; Unitary completion; Unitary matrices

Indexed keywords

EID: 38849165935     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-07-02004-2     Document Type: Article

References (12)

1. D. A. Bini, Y. Eidelman, L. Gemignani and I. Gohberg, Fast QR eigenvalue algorithms for Hessenberg matrices which are rank-one perturbations of unitary matrices, Technical report 1587, Dipartimento di Matematica, Universita di Pisa, 2005.
2. D. A. Bini, F. Daddi, and L. Gemignani. On the shifted QR iteration applied to companion matrices. Electron. Trans. Numer. Anal., 18:137-152, 2004. MR2133492 (2005m:65076)
3. D. Calvetti, S. Kim, and L. Reichel. The restarted QR-algorithm for eigenvalue computation of structured matrices. J. Comput. Appl. Math., 149:415-422, 2002. MR1937292 (2003i:65034)
4. H. Dym and I. Gohberg, Extensions of matrix valued functions and block matrices, Indiana University Mathematics Journal 31: 733-765 (1982). MR667792 (84g:47035)
5. Y. Eidelman and I. Gohberg, On a new class of structured matrices. Integral Equations and Operator Theory 34: 293-324 (1999). MR1689391 (2000e:15020)
6. Y. Eidelman and I. Gohberg, Direct approach to the band completion problem. Linear Algebra and Application 385: 149-185 (2004). MR2063354 (2005b:15047)
7. P. E. Gill, G. H. Golub, W. Murray, and M. A. Saunders. Methods for modifying matrix factorizations. Math. Comp., 28:505-535, 1974. MR0343558 (49:8299)
8. W. B. Gragg, The QR algorithm for unitary Hessenberg matrices, Journal of Computational and Applied Mathematics 16: 1-8 (1986).
9. G. H. Golub and C. F. Van Loan, Matrix Computations, John Hopkins, Baltimore 1983. MR733103 (85h:65063)
10. M. Stewart, Stability properties of several variants of the unitary Hessenberg QR algorithm, Contemporary Mathematics 281: 57-72 (2001). MR1855505 (2002f:65055)
11. D. S. Watkins. Fundamentals of matrix computations. Wiley-Interscience [John Wiley & Sons], New York, 2002. MR1899577 (2003a:65002)
12. J. H. Wilkinson. The algebraic eigenvalue problem. Monographs on Numerical Analysis. The Clarendon Press Oxford University Press, New York, 1988. Oxford Science Publications. MR950175 (89j:65031)