| Project/Area Number |
23654040
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Keio University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TANI Atsushi 慶應義塾大学, 理工学部, 名誉教授 (90118969)
OHNO Yoshio 慶應義塾大学, 理工学部, 名誉教授 (20051865)
YAMAMOTO Yoshikazu 慶應義塾大学, 理工学部, 旧教授 (20051873)
TAMURA Youzou 慶應義塾大学, 理工学部, 教授 (50171905)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 非適切な問題 / 離散型悪条件問題 / 逆問題 / GMRES / Krylov部分空間 / Tikhonov正則化 / 制約条件 / augmentation / GMRES法 / Tikhonov正則化法 / 線形悪条件問題 / Tikhonov値 / 並列計算 / 非適切問題 / 正則化法 / Tikhonov |
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| Research Abstract |
GMRES regularization method is arguably the most popular solution for linear discrete ill-posed problems. We explores different regularization methods as a means of yielding stable solutions for linear discrete ill-posed problems.
The regularization with GMRES must be implemented in two stages, which are designed to generate an approximate solution of a linear system through the use of GMRES, and to determine the most appropriate solution by using a constraint. In the first stage, particular behaviors of GMRES and preconditioned GMRES for linear discrete ill-posed problems are identified. In the second stage, a simplified Tikhonov threshold as a constraint to determine the best approximate solution is explored. Numerical experiments have been tabulated to underline the effectiveness of our proposed method.
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