| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
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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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