Name
Abstract | ||
|---|---|---|
The matrix Sylvester equation for congruence, or T-Sylvester equation, has recently attracted considerable attention as a consequence of its close relation to palindromic eigenvalue problems. The theory concerning T-Sylvester equations is rather well understood, and there are stable and efficient numerical algorithms which solve these equations for small- to medium-sized matrices. However, developing numerical algorithms for solving large-scale T-Sylvester equations still remains an open problem. In this paper, we present several projection algorithms based on different Krylov spaces for solving this problem when the right-hand side of the T-Sylvester equation is a low-rank matrix. The new algorithms have been extensively tested, and the reported numerical results show that they work very well in practice, offering clear guidance on which algorithm is the most convenient in each situation. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1090/mcom/3081 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
Matrix equations,Krylov subspace,iterative methods,large-scale equations,Sylvester equation,Sylvester equation for congruence | Krylov subspace,Mathematical optimization,Sylvester equation,Open problem,Mathematical analysis,Iterative method,Matrix (mathematics),Mathematics,Independent equation,Eigenvalues and eigenvectors,Simultaneous equations | Journal |
Volume | Issue | ISSN |
85 | 301 | 0025-5718 |
Citations | PageRank | References |
1 | 0.36 | 13 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Froilán M. Dopico | 1 | 98 | 14.08 |
| Javier González | 2 | 34 | 5.17 |
| Daniel Kressner | 3 | 449 | 48.01 |
| Valeria Simoncini | 4 | 384 | 35.15 |