Implicitly Restarted And Refined Global Lanczos Method And Block Lanczos Method

Numerical methods for solving large symmetric eigenvalue problems are considered in this thesis.Based on the developed global Lanczos process, a global Lanczos method for solving large symmetriceigenvalue problems is presented. In order to accelerate the convergence of the F-Ritz vectors, therefined global Lanczos method is developed. In order to compute a few of extreme eigenvalues andreduce the computational cost, an approach for computing refined shifts of the refined global methodis presented. Combining the implicitly restarted strategy with the deflation technique, an implicitlyrestarted and refined global Lanczos method for computing some eigenvalues of large symmetricmatrices is proposed.A refined technique is developed for the block Lanczos method for solving large symmetriceigenvalue problems. We apply the implicitly restarted strategy with refined shifts and the deflationtechnique to the block Lanczos method, and present implicitly restarted and refined block Lanczosmethod.Numerical results show that the proposed methods are efficient.