Name
Abstract | ||
|---|---|---|
We extend the Rayleigh-Ritz method to the eigen-problem of periodic matrix pairs. Assuming that the deviations of the desired periodic eigenvectors from the corresponding periodic subspaces tend to zero, we show that there exist periodic Ritz values that converge to the desired periodic eigenvalues unconditionally, yet the periodic Ritz vectors may fail to converge. To overcome this potential problem, we minimize residuals formed with periodic Ritz values to produce the refined periodic Ritz vectors, which converge under the same assumption. These results generalize the corresponding well-known ones for Rayleigh-Ritz approximations and their refinement for non-periodic eigen-problems. In addition, we consider a periodic Arnoldi process which is particularly efficient when coupled with the Rayleigh-Ritz method with refinement. The numerical results illustrate that the refinement procedure produces excellent approximations to the original periodic eigenvectors. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.cam.2010.11.014 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
original periodic eigenvectors,rayleigh-ritz method,periodic matrix pair,corresponding periodic subspaces,periodic eigenvectors,periodic ritz vector,periodic arnoldi process,periodic ritz value,periodic ritz,periodic eigenvalues,eigenvalues,eigenvectors,rayleigh ritz method,refinement | Rayleigh–Ritz method,Mathematical analysis,Matrix (mathematics),Ritz method,Numerical analysis,Periodic sequence,Periodic graph (geometry),Numerical linear algebra,Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
235 | 8 | 0377-0427 |
Citations | PageRank | References |
0 | 0.34 | 9 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Eric King-wah Chu | 1 | 88 | 11.99 |
| Hung-Yuan Fan | 2 | 31 | 6.24 |
| Zhongxiao Jia | 3 | 121 | 18.57 |
| Tiexiang Li | 4 | 29 | 5.19 |
| Wen-wei Lin | 5 | 456 | 67.35 |