Name
Abstract | ||
|---|---|---|
We analyze the stability of a class of eigensolvers that target interior eigenvalues with rational filters. We show that subspace iteration with a rational filter is robust even when an eigenvalue is near a filter's pole. These dangerous eigenvalues contribute to large round-off errors in the first iteration but are self-correcting in later iterations. For matrices with orthogonal eigenvectors (e.g., real-symmetric or complex Hermitian), two iterations are enough to reduce round-off errors to the order of the unit round-off. In contrast, Krylov methods accelerated by rational filters with fixed poles typically fail to converge to unit round-off accuracy when an eigenvalue is close to a pole. In the context of Arnoldi with shift-and-invert enhancement, we demonstrate a simple restart strategy that recovers full precision in the target eigenpairs. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1137/20M1385330 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | DocType | Volume |
subspace iteration, Arnoldi, shift-and-invert, rational filters, FEAST, CIRR | Journal | 43 |
Issue | ISSN | Citations |
1 | 0895-4798 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andrew Horning | 1 | 1 | 0.71 |
| Yuji Nakatsukasa | 2 | 97 | 17.74 |