| Title:
|
Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem (English) |
| Author:
|
Chen, Hongjia |
| Author:
|
Imakura, Akira |
| Author:
|
Sakurai, Tetsuya |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2017 |
| Pages:
|
357-375 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
One of the most efficient methods for solving the polynomial eigenvalue problem (PEP) is the Sakurai-Sugiura method with Rayleigh-Ritz projection (SS-RR), which finds the eigenvalues contained in a certain domain using the contour integral. The SS-RR method converts the original PEP to a small projected PEP using the Rayleigh-Ritz projection. However, the SS-RR method suffers from backward instability when the norms of the coefficient matrices of the projected PEP vary widely. To improve the backward stability of the SS-RR method, we combine it with a balancing technique for solving a small projected PEP. We then analyze the backward stability of the SS-RR method. Several numerical examples demonstrate that the SS-RR method with the balancing technique reduces the backward error of eigenpairs of PEP. (English) |
| Keyword:
|
SS-RR method |
| Keyword:
|
polynomial eigenvalue problem |
| Keyword:
|
balancing technique |
| MSC:
|
15A18 |
| MSC:
|
65F15 |
| idZBL:
|
Zbl 06770049 |
| idMR:
|
MR3686422 |
| DOI:
|
10.21136/AM.2017.0016-17 |
| . |
| Date available:
|
2017-08-31T12:45:11Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146834 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
