The QR iteration method for Hermitian quasiseparable matrices of an arbitrary order

Linear Algebra and Its Applications

Volumn 404, Issue 1-3, 2005, Pages 305-324

  Eidelman, Yuli ^a   Gohberg, Israel ^a   Olshevsky, Vadim ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Eigenvalue problem; QR iteration; Quasiseparable matrices; Semiseparable matrices; Tridiagonal matrices

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; LINEAR ALGEBRA; MATHEMATICAL MODELS; NUMBER THEORY; NUMERICAL ANALYSIS; PROBLEM SOLVING;

EIGENVALUE PROBLEM; QR ITERATION; QUASISEPARABLE MATRICES; SEMISEPARABLE MATRICES; TRIDIAGONAL MATRICES;

MATRIX ALGEBRA;

EID: 20344378938     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2005.02.037     Document Type: Article

References (19)

1. D. Bini, F. Daddi, L. Gemignani, On the shifted QR iteration applied to Frobenius matrices, Tech. Report 1483, Department of Mathematics, University of Pisa, 2003
2. D. Bini, L. Gemignani, V. Pan, QR-like algorithms for generalized semiseparable matrices, Tech. Report 1470, Department of Mathematics, University of Pisa, 2004
3. S. Chandrasekaran, and M. Gu Fast and stable eigendecomposition of symmetric banded plus semi-separable matrices Linear Algebra Appl. 313 2000 107 114
4. S. Chandrasekaran, and M. Gu A divide-and-conquer algorithm for the eigendecomposition of symmetric block- diagonal plus semi-separable matrices Numer. Math. 96 2004 723 731
5. P.M. Dewilde, and A.J. van der Veen Time-varying Systems and Computations 1998. Kluwer
6. Y. Eidelman, and I. Gohberg Fast inversion algorithms for diagonal plus semiseparable matrices Integral Equations Operator Theory 27 1997 165 183
7. Y. Eidelman, and I. Gohberg On a new class of structured matrices Integral Equations Operator Theory 34 1999 293 324
8. Y. Eidelman, and I. Gohberg Linear complexity inversion algorithms for a class of structured matrices Integral Equations Operator Theory 35 1999 28 52
9. Y. Eidelman, and I. Gohberg A modification of the Dewilde-van der Veen method for inversion of finite structured matrices Linear Algebra Appl. 343-344 2002 419 450
10. D. Fasino, Rational Krylov matrices and QR steps on Hermitian diagonal-plus-semiseparable matrices, Numer. Linear Algebra Appl., 2003, to appear
11. D. Fasino, N. Mastronardi, and M. Van Barel Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form Contemp. Math. 323 2003 105 118
12. F.R. Gantmacher, and M.G. Krein Sur les matrices oscillatoires et complétement non négatives Compositio Math. 4 1937 445 476 54, 73
13. N. Mastronardi, S. Chandrasekaran, and S. Van Huffel Fast and stable reduction of diagonal plus semiseparable matrices to tridiagonal and bidiagonal form BIT 41 2001 149 157
14. N. Mastronardi, E. Van Camp, M. Van Barel, Divide and conquer type algorithms for computing the eigendecomposition of diagonal plus semiseparable matrices, Tech. Report 7(5/2003), Instituto per le Applicazioni del Calcolo M. Picone, Consiglio Nazionale delle Ricerche, Rome, Italy, 2003
15. J. Stoer, and R. Bulirsch Introduction to Numerical Analysis 1993 Springer-Verlag New York London
16. E.E. Tyrtyshnikov Mosaic ranks for weakly semiseparable matrices M. Griebel S. Margenov P. Yalamov Large-scale Scientific Computations of Engineering and Environmental Problems II Notes on Numerical Fluid Mechanics vol. 73 2000 Vieweg 36 41
17. R. Vandebril, Semiseparable Matrices and the Symmetric Eigenvalue Problem, Katholieke Universiteit Leuven, 2004
18. R. Vandebril, M. Van Barel, N. Mastronardi, An implicit QR-algorithm for semiseparable matrices to compute the eigendecomposition of symmetric matrices, Tech. Report TW367, Department of Computer Science, Katholieke Universiteit Leuven, 2003
19. R. Vandebril, M. Van Barel, N. Mastronardi, A note on the representation and definition of semiseparable matrices, Tech. Report TW368, Department of Computer Science, Katholieke Universiteit Leuven, 2003