Perturbation bounds of the Krylov bases and associated Hessenberg forms

Linear Algebra and Its Applications

Volumn 265, Issue 1-3, 1997, Pages 1-28

  Kuznetsov, S V ^a  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21744435663     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(96)00299-6     Document Type: Article

References (9)

1. W. E. Arnoldi, The principle of minimized iteration in the solution of the matrix eigenvalue problem, Quart. Appl. Math. 9:17-29 (1951).
2. M. Berger, Geometrie, Nathan, Paris, 1977.
3. J. F. Carpraux, S. Godunov, and S. Kuznetsov, Stability of the Krylov Bases and Subspaces, Linear Algebra Appl, 248:137-161 (1996).
4. G. H. Golub and C. F. Van Loan, Matrix Computations, Johns Hopkins U.P., Baltimore, 1989.
5. S. K. Godunov, A. G. Antonov, O. P. Kirilyuck, and V. I. Kostin, Guaranteed Accuracy in Numerical Linear Algebra, Kluwer Academic, Dordrecht, 1993.
6. A. N. Krylov, On the numerical solution of equations whose solution determines the frequency of small vibrations of material systems (in Russian), Izv. Akad. Nauk. SSSR Otd. Mat. Estest. 1:491-539 (1931).
7. P. Lancaster and M. Tismenetsky, The Theory of Matrices, Academic, New York, 1985.
8. G. W. Stewart and Ji-guang Sun, Matrix Perturbation Theory, Academic, 1990.
9. J. H. Wilkinson, Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, N.J., 1963.