A matrix analysis of Arnoldi and Lanczos methods

Numerische Mathematik

Volumn 81, Issue 1, 1998, Pages 125-141

  Simoncini, V ^a  

^a CNR   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032263789     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050386     Document Type: Article

References (21)

1. Arnoldi, W.E. (1951): The principle of minimized iteration in the solution of the matrix eigenvalue problem. Quart. Appl. Math. 9, 17-29
2. Beam, R.M., Warming, R.F. (1993): The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices. SIAM J. Sci. Comput. 14, 971-1006
3. Björck, A. (1994): Numerics of Gram-Schmidt Orthogonalization. Linear Algebra Appl. 197 297-316
4. Chaitin-Chatelin, F., Fraysse, V. (1996): Lectures on Finite Precision Computations, SIAM, Philadelphia
5. Cullum, J. (1996): Arnoldi versus nonsymmetric Lanczos algorithms for solving matrix eigenvalue problems. Tech. rep., IBM Research
6. Freund, R.W., Nachtigal, N.M. (1995): Software for simplified Lanczos and QMR algorithms. Applied Numerical Mathematics 19, 319-341
7. Golub, G., Van Loan, C.F. (1989): Matrix Computations, 2nd edn. The Johns Hopkins University Press, Baltimore
8. Householder, A.S. (1975): The Theory of Matrices in Numerical Analysis. Dover Publ. Inc.
9. Kahan, W., Parlett, B.N., Jiang, E. (1982): Residual bounds on approximate eigensystems of nonnormal matrices. SIAM J. Numer. Anal. 19, 470-484
10. Lanczos, C. (1950): An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Natl. Bur. Stand. 45, 255-282
11. Parlett, B.N., Scott, C.S. (1979): The Lanczos algorithm with selective orthogonalization. Math. of Comp. 33, 217-238
12. Parlett, B.N., Taylor, D.R., Liu, Z.A. (1985): A look-ahead Lanczos algorithm for unsymmetric matrices. Math. Comp. 44, 105-124
13. Reddy, S.C., Trefethen, L.N. (1990): Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues. Comput. Meth. Appl. Mech. Eng. 80, 147-164
14. Reichel, L, Trefethen, L.N: (1992): Eigenvalues and pseudo-eigenvalues of Toeplitz matrices. Lin. Alg. Appl. 162-164, 153-185
15. Ruhe, A. (1983): The two-sided Arnoldi algorithm for nonsymmetric eigenvalue problems. In: Kågström, B., Ruhe, A. (eds) Matrix Pencils. Springer-Verlag, Berlin. Lecture Notes in Mathematics, vol. 973, Proceedings, Pite Havsbad, 1982
16. Saad, Y. (1983): Projection methods for solving large sparse eigenvalue problems. In: Kågström, B., Ruhe, A. (eds) Matrix Pencils, vol. 973 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, pp. 121-144
17. Saad, Y. (1992): Numerical Methods for Large Eigenvalue Problems. Halsted Press, New York
18. Stewart, G.W., Sun, J.-G. (1990): Matrix Perturbation Theory. Academic Press
19. Sun, J.-G. (1993): Backward perturbation analysis of certain characteristic subspaces. Numer. Math. 65, 357-382
20. Toh, K., Trefethen, L.N. (1996): Calculation of pseudospectra by the Arnoldi iteration. SIAM J. Sci. Comput. 17, 1-15
21. Trefethen, L.N. (1990): Approximation theory and numerical linear algebra. In: Mason, J.C., Cox, M.G. (eds) Algorithms for Approximation II. Chapman and Hall, London