2016 Fiscal Year Final Research Report
Numerical methods achieving higher accuracy than the Sinc numerical methods
| Project/Area Number |
25390146
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Computational science
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| Research Institution | Aoyama Gakuin University |
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Principal Investigator |
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| Research Collaborator |
TANAKA Ken'ichiro
OKAYAMA Tomoaki
SUGITA Kosuke
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 関数近似 / 数値積分 / Sinc関数近似 / DE変換 / 最適関数近似 / 最適数値積分公式 |
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| Outline of Final Research Achievements |
Sinc numerical methods is a general term for numerical methods using Sinc approximation. They are extremely effective for analytic functions, and are known to be robust even when function has singularities. It is also shown that the Sinc approximation is nearly optimal in theory. In this research, we develope numerical methods achieving higher accuracy than the Sinc numerical methods. Specifically, we develope a function approximation formula achieving higher accuracy than the Sinc approximation, more precisely, an optimal approximation formula. Futher, based on the knowledge obtained there, we establish a theory of the optimal numerical integration and based on the theory, a numerical integration formula expected to be close to optimal is obtained by numerical calculation. We also develope a methodology based on the potential theory that designs optimal formulas in a unified way.
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| Free Research Field |
数値解析学
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