2009 Fiscal Year Final Research Report
Establishment of Verified Numerical Computation
| Project/Area Number |
17002012
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| Research Category |
Grant-in-Aid for Specially Promoted Research
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
Engineering
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| Research Institution | Waseda University |
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Principal Investigator |
OISHI Shin'ichi Waseda University, 理工学術院, 教授 (20139512)
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| Co-Investigator(Renkei-kenkyūsha) |
NAKAO Mitsuhiro 九州大学, 数理学研究院, 教授 (10136418)
NISHIDA Takaaki 早稲田大学, 理工学術院, 教授 (70026110)
SHIBATA Yoshihiro 早稲田大学, 理工学術院, 教授 (50114088)
YAMAMOTO Nobito 電気通信大学, 電気通信学部, 教授 (30210545)
WATANABE Yoshitaka 九州大学, 情報基盤研究開発センター, 准教授 (90243972)
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| Project Period (FY) |
2005 – 2009
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| Keywords | 数値解析 / 数値計算 / 非線形方程式 / 情報数理 / アルゴリズム |
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| Research Abstract |
Establishment of Verified Numerical Computation We have studied verified numerical computations for partial differential equations and systems of linear equations using digital computers. Calculating sum of a vector and dot product of two vectors with guaranteed high accuracy is ubiquitous in scientific computing. We have developed such algorithms for accurate sum and dot product, which are known to be the fastest so far. As applications, we have applied the fast and accurate algorithms to sparse matrix computations, computational geometry and so forth. Moreover, we have succeeded in proving the existence and uniqueness of a solution of a partial differential equation, and in calculating an error bound of its approximate solution.
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