2012 Fiscal Year Final Research Report
Study on fast and robust iterative methods for solving large and sparse shifted linear systems arising from computational science
| Project/Area Number |
21760058
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Engineering fundamentals
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| Research Institution | Aichi Prefectural University |
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Principal Investigator |
SOGABE Tomohiro 愛知県立大学, 大学院・情報科学研究科, 准教授 (30420368)
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| Project Period (FY) |
2009 – 2012
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| Keywords | シフト線形方程式 / クリロフ部分空間法 / COCR 法 / Bi-CR 法 |
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| Research Abstract |
We developed some efficient iterative methods for solving large and sparse shifted linear systems that arise from computational science. As a result, the shifted COCR method was proposed for solving complex symmetric case, and a variant of the shifted GMRES method was proposed for (complex) nonsymmetric case. Remarkably, the shifted COCR method was about 26 times faster than the COCR method for a problem arising from large scale electronic structure calculation. As related work, the following results are obtained: (1) An improvement of the COCR method for solving complex symmetric linear systems; (2) Improvements of the IDR method; (3) An improvement of the GMRES(m) method for solving nonsymmetric linear systems; (4) a fast solver for linear systems with a special matrix; (5) Efficient iterative method for generalized shifted linear systems with complex symmetric matrices.
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