Name
Abstract | ||
|---|---|---|
. Generalized block Lanczos methods for large unsymmetric eigenproblems are presented, which contain the block Arnoldi method,
and the block Arnoldi algorithms are developed. The convergence of this class of methods is analyzed when the matrix A is diagonalizable. Upper bounds for the distances between normalized eigenvectors and a block Krylov subspace are derived,
and a priori theoretical error bounds for Ritz elements are established. Compared with generalized Lanczos methods, which
contain Arnoldi's method, the convergence analysis shows that the block versions have two advantages: First, they may be efficient
for computing clustered eigenvalues; second, they are able to solve multiple eigenproblems. However, a deep analysis exposes
that the approximate eigenvectors or Ritz vectors obtained by general orthogonal projection methods including generalized
block methods may fail to converge theoretically for a general unsymmetric matrix A even if corresponding approximate eigenvalues or Ritz values do, since the convergence of Ritz vectors needs more sufficient
conditions, which may be impossible to satisfy theoretically, than that of Ritz values does. The issues of how to restart
and to solve multiple eigenproblems are addressed, and some numerical examples are reported to confirm the theoretical analysis. |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1007/s002110050367 | Numerische Mathematik |
Keywords | DocType | Volume |
krylov subspace,orthogonal projection,eigenvalues,upper bound,eigenvectors,satisfiability | Journal | 80 |
Issue | ISSN | Citations |
2 | 0029-599X | 5 |
PageRank | References | Authors |
1.33 | 3 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhongxiao Jia | 1 | 121 | 18.57 |