On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods TeX Export

@article{citeulike:1157576, abstract = {Theoretical error bounds are established, improving those given by S. Kaniel. Similar inequalities are found for the eigenvectors by using bounds on the acute angle between the exact eigenvectors and the Krylov subspace spanned by \$x\_0 ,Ax\_0 , \cdots ,A^{n - 1} x\_0 \$, where \$x\_0 \$ is the initial vector of the process.All the results obtained are then extended to the block-Lanczos method, and it is shown that the bounds on the rates of the Block version are superior to those of the single vector process. The difference between the two methods is in many respects similar to the difference between the simultaneous iteration method and the single vector power method. Several numerical experiments are described in order to compare the actual rates of convergence with the theoretical bounds.}, citeulike-article-id = {1157576}, citeulike-linkout-0 = {http://dx.doi.org/10.1137/0717059}, doi = {10.1137/0717059}, editor = {Sia, M.}, journal = {Journal on Numerical Analysis}, keywords = {block, convergence, lanczos, subspace}, number = {5}, pages = {687--706}, posted-at = {2007-03-13 07:11:53}, priority = {5}, title = {On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods}, url = {http://dx.doi.org/10.1137/0717059}, volume = {17}, year = {1980} }

TY - JOUR ID - citeulike:1157576 L3 - citeulike-article-id:1157576 N2 - Theoretical error bounds are established, improving those given by S. Kaniel. Similar inequalities are found for the eigenvectors by using bounds on the acute angle between the exact eigenvectors and the Krylov subspace spanned by $x_0 ,Ax_0 , \cdots ,A^{n - 1} x_0 $, where $x_0 $ is the initial vector of the process.All the results obtained are then extended to the block-Lanczos method, and it is shown that the bounds on the rates of the Block version are superior to those of the single vector process. The difference between the two methods is in many respects similar to the difference between the simultaneous iteration method and the single vector power method. Several numerical experiments are described in order to compare the actual rates of convergence with the theoretical bounds. IS - 5 JF - Journal on Numerical Analysis EP - 706 TI - On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods VL - 17 SP - 687 KW - block KW - convergence KW - lanczos KW - subspace A2 - Sia, M PY - 1980/// UR - http://dx.doi.org/10.1137/0717059 ER -