Adjusting the Rayleigh quotient in semiorthogonal Lanczos methods

SIAM Journal on Scientific Computing

Volumn 24, Issue 1, 2003, Pages 201-207

  Stewart, G W ^a  

^a Institute of Advanced Computer Science   (United States)

Author keywords

Adjusted Rayleigh quotient; Lanczos method; Large eigenproblem; Partial reorthogonalization; Symmetric matrix

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; ESTIMATION; MATRIX ALGEBRA; PROBLEM SOLVING; VECTORS;

LANCZOS ALGORITHMS; RAYLEIGH QUOTIENT; RITZ VECTORS; TRIDIAGONAL MATRIX;

ALGORITHMS;

EID: 0037249816     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827501388984     Document Type: Article

References (6)

1. J. Grcar, Analyses of the Lanczos Algorithm and of the Approximation Problem in Richardson's Method, Ph.D. thesis, University of Illinois at Urbana-Champaign, 1981.
2. Z. Jia and G. W. Stewart, An analysis of the Rayleigh-Ritz method for approximating eigenspaces, Math. Comp., 70 (2001), pp. 637-647.
3. Y. Saad, Numerical Methods for Large Eigenvalue Problems: Theory and Algorithms, John Wiley, New York, 1992.
4. H. D. Simon, Analysis of the symmetric Lanczos algorithm with reorthogonalization methods, Linear Algebra Appl., 61 (1984), pp. 101-132.
5. H. D. Simon, The Lanczos algorithm with partial reorthogonalization, Math. Comp., 42 (1984), pp. 115-142.
6. G. W. Stewart, A Krylov-Schur algorithm for large eigenproblems, SIAM J. Matrix Anal. Appl., 23 (2001), pp. 601-614.