van Dorsselaer, Jos L. M.; Hochstenbach, Michiel E.; van der Vorst, Henk A. Computing probabilistic bounds for extreme eigenvalues of symmetric matrices with the Lanczos method. (English) Zbl 0981.65044 SIAM J. Matrix Anal. Appl. 22, No. 3, 837-852 (2001). The paper deals with computing extreme eigenvalues of symmetric matrices using the Lanczos method. The authors compute probabilistic bounds for the extreme eigenvalues using data available during the execution of the Lanczos method, and four different bounds are obtained using Lanczos, Ritz, and Chebyshev polynomials. Reviewer: Emil Minchev (Sofia) Cited in 9 Documents MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices Keywords:symmetric and Hermitian matrices; eigenvalues; Lanczos method; Ritz values; probabilistic eigenvalue bounds; misconvergence; Lanczos polynomials; Ritz polynomials PDFBibTeX XMLCite \textit{J. L. M. van Dorsselaer} et al., SIAM J. Matrix Anal. Appl. 22, No. 3, 837--852 (2000; Zbl 0981.65044) Full Text: DOI