Volume 18, Issue 4
Preconditioning Block Lanczos Algorithm for Solving Symmetric Eigenvalue Problems

Hua Dai & Peter Lancaster

DOI:

J. Comp. Math., 18 (2000), pp. 365-374

Published online: 2000-08

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  • Abstract

A preconditioned iterative method for computing a few eigenpairs of large sparse symmetric matrices is presented in this paper. The proposed method which combines the preconditioning techniques with the efficiency of block Lanczos algorithm is suitable for determination of the extreme eigenvalues as well as their multiplicities. The global convergence and the asymptotically quadratic convergence of the new method are also demonstrated.

  • Keywords

eigenvalue eigenvector sparse matrices Lanczos method preconditioning

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@Article{JCM-18-365, author = {}, title = {Preconditioning Block Lanczos Algorithm for Solving Symmetric Eigenvalue Problems}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {4}, pages = {365--374}, abstract = { A preconditioned iterative method for computing a few eigenpairs of large sparse symmetric matrices is presented in this paper. The proposed method which combines the preconditioning techniques with the efficiency of block Lanczos algorithm is suitable for determination of the extreme eigenvalues as well as their multiplicities. The global convergence and the asymptotically quadratic convergence of the new method are also demonstrated. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9049.html} }
TY - JOUR T1 - Preconditioning Block Lanczos Algorithm for Solving Symmetric Eigenvalue Problems JO - Journal of Computational Mathematics VL - 4 SP - 365 EP - 374 PY - 2000 DA - 2000/08 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9049.html KW - eigenvalue KW - eigenvector KW - sparse matrices KW - Lanczos method KW - preconditioning AB - A preconditioned iterative method for computing a few eigenpairs of large sparse symmetric matrices is presented in this paper. The proposed method which combines the preconditioning techniques with the efficiency of block Lanczos algorithm is suitable for determination of the extreme eigenvalues as well as their multiplicities. The global convergence and the asymptotically quadratic convergence of the new method are also demonstrated.
Hua Dai & Peter Lancaster. (1970). Preconditioning Block Lanczos Algorithm for Solving Symmetric Eigenvalue Problems. Journal of Computational Mathematics. 18 (4). 365-374. doi:
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