2006 Fiscal Year Final Research Report Summary
Synthetical development of fast numerical methods for solving large-scale linear systems which arise g from the field of computational science and engineerin
| Project/Area Number |
15360042
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Nagoya University (2005-2006)
The University of Tokyo (2003-2004) |
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Principal Investigator |
ZHANG Shao-liang Nagoya University, Graduate School of Engineering, Professor, 大学院工学研究科, 教授 (20252273)
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| Co-Investigator(Kenkyū-buntansha) |
OYANAGI Yoshio Kogakuin University, Faculty of Informatics, professor, 情報学部, 教授 (60011673)
FUJINO Seiji Kyusyu University, Computing and Communications Center, Professor, 情報基盤センター, 教授 (40264965)
HAYAMI Ken National Institute of Informatics, Principles of Informatics Research Division, Professor, 情報学基礎研究系, 教授 (20251358)
HASEGAWA Hidehiko University of Tsukuba, Graduate school of Library Information and Media Studies, Associate Professor, 図書館情報学系, 助教授 (20164824)
ABE Kuniyoshi Gifu Shotoku Gakuen, Economics and Information, Associate Professor, 経済情報学部, 助教授 (10311086)
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| Project Period (FY) |
2003 – 2006
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| Keywords | large-scale 1inear systems / fast numerical method / Krylov-subspace method / preconditioning technique / super computer / parallel computer / singular matrix / library |
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| Research Abstract |
The target of this project is synthetically to develop fast numerical methods for solving large-scale linear systems which arise from the field of computational science and engineering. Throughout the whole of this project, we completed almost the target.
The research results of this project are concluded as follows.
1. The circumstance of applications which lead large linear systems was investigated by all of numbers.
2. The coefficient matrix of linear systems was classified from size, structure and algebra.
3. The convergent property of new methods GPBi-CG(ω) and GPBi-CG was evaluated through many test problems.
4. The convergence theory for singular linear systems was studied.
5. Several kinds of preconditioning technique was studied.
6. A new fast and basic method, so-called Bi-CR, was proposed.
7. A new systems of parallel computer was built for this project.
8. A new web server system for large linear system was built almost.
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