2012 Fiscal Year Final Research Report
Developments of new linear solvers based on the induced dimension reduction theorem
| Project/Area Number |
22560067
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | Gifu Shotoku Gakuen University |
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Principal Investigator |
ABE Kuniyoshi 岐阜聖徳学園大学, 経済情報学部, 教授 (10311086)
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| Co-Investigator(Kenkyū-buntansha) |
FUJINO Seiji 九州大学, 情報基盤センター, 教授 (40264965)
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| Co-Investigator(Renkei-kenkyūsha) |
ISHIWATA Emiko 東京理科大学, 理学部, 教授 (30287958)
NAKAJIMA Kengo 東京大学, 情報基盤センター, 教授 (20376528)
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| Research Collaborator |
SLEIJPEN Gerard L,G. Utrecht University, Department of Math., Associate Professor
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| Project Period (FY) |
2010 – 2012
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| Keywords | 線形方程式 / Krylov 空間法 / 帰納的次元縮小(IDR)定理 / IDR(s)法 / 一般化積型解 法 (GPBiCG) / IDRstab 法 / スムージング技法 / ブロック IDR(s)法 |
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| Research Abstract |
Krylov subspace methods, specifically hybrid Bi-CG methods, have been developed in the 1990s, and some advantages with the hybrid BiCG methods are well-known. A new method which is called the Induced Dimension Reduction (abbreviated to IDR) (s) has been proposed in 2007. It has recently reported that the IDR(s) method sometimes converges faster than the hybrid Bi-CG methods. Many researchers have focused on the IDR(s) method. Therefore, by combining the advantage of IDR(s) with that of the hybrid Bi-CG methods, we have proposed new solvers which have better convergence than the hybrid Bi-CG and original IDR(s) methods.
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