2005 Fiscal Year Final Research Report Summary
Study on solution of nonlinear equations and development of their practical software
| Project/Area Number |
15560049
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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 | University of Tsukuba |
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Principal Investigator |
SAKURAI Tetsuya University of Tsukuba, Graduate School of Systems and Information Engineering, Professor, 大学院・システム情報工学研究科, 教授 (60187086)
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| Co-Investigator(Kenkyū-buntansha) |
KITAGAWA Tahashi University of Tsukuba, Graduate School of Systems and Information Engineering, Professor, 大学院・システム情報工学研究科, 教授 (60153095)
SUGIURA Hiroshi Nanzan University, Faculty of Mathematical Sciences and Information Engineering, Professor, 数理情報学部, 教授 (60154465)
SUZUKI Tomohiro Yamanashi University, Faculty of Engineering, Research Assistant, 工学部, 助手 (70235977)
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| Project Period (FY) |
2003 – 2005
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| Keywords | Nonlinear Equations / Iterative Methods / Validation / Practical Software |
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| Research Abstract |
In this research project, we considered iterative solver for nonlinear equations and their applications. We also develop practical software and apply them for various problems. We obtained factoring methods which can provide factors of close zeros with verification. In ordinary methods such as verified Newton's method, the verification for close zeros was a difficult problem. We proposed some algorithms to estimate parameters for verification. Software using MATLAB and INTLAB were developed, and efficiency of this method was considered by numerical experiments. We also apply our method for large-scale eigenvalue problems. This method is suitable for parallel computing in a grid computing environment. We implemented the algorithm with a hybrid of Grid RPC system and MPI. In the application of large molecular orbital computations, we obtained high performance with our method. An system environment to support development of mathematical software with graphical user interface was provided. On this system, we developed some mathematical algorithms.
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Research Products
(66 results)
