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A new shift strategy for the implicitly restarted generalized second-order Arnoldi method
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gong, Fanghui Sun, Yuquan |
| Copyright Year | 2017 |
| Abstract | In this paper, a new shift strategy for the implicitly restarted generalized second-order Arnoldi (GSOAR) method is proposed. In implicitly restarted processes, we can get a $k$-step GSOAR decomposition from a $m$-step GSOAR decomposition by performing $p = m-k$ implicit shifted QR iterations. The problem of the implicitly restarted GSOAR is the mismatch between the number of shifts and the dimension of the subspace. There are $2p$ shifts for $p$ QR iterations. We use the shifts to filter out the unwanted information in the current subspace; when more shifts are used, one obtains a better updated subspace. But, if we use more than $p$ shifts, the structure of the GSOAR decomposition will be destroyed. We propose a novel method which can use all $2p$ candidates and preserve the special structure. The new method vastly enhances the overall efficiency of the algorithm. Numerical experiments illustrate the efficiency of every restart process. |
| Starting Page | 635 |
| Ending Page | 650 |
| Page Count | 16 |
| File Format | PDF HTM / HTML |
| DOI | 10.1360/012016-22 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1701.03042v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1360/012016-22 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
