Optimal estimation for inverse of infinite-dimensional operator by self-validating numerical computations and its applications
| Project/Area Number |
24340018
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
Nagatou Kaori 九州大学, マス・フォア・インダストリ研究所, 准教授 (40326426)
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| Co-Investigator(Renkei-kenkyūsha) |
Nakao Mitsuhiro T. 佐世保工業高等専門学校, 校長 (10136418)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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| Keywords | 精度保証付き数値計算 / 偏微分方程式 / 計算機援用証明 / 関数解析 / 無限次元固有値問題 / 不動点定理 / 応用数学 / 関数方程式論 / 微分方程式 / 精度保証 / 非線形解析 / 固有値解析 |
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| Outline of Final Research Achievements |
"Self-validating numerical computations" stands for a computer-assisted approach to prove the existence of the solutions and its guaranteed error bounds for a given problem. By using self-validating numerical computations, this reserch proposed a computer-assisted procedure to assure the invertibility of a linear operator which is the sum of an unbounded bijective and a bounded operator in a Hilbert space, and to compute a bound for the norm of its inverse. We also showed that our bounds are expected to converge to the exact operator norm and to provide accurate and efficient enclosure results for the solution of nonlinear problem by infinite-dimensional Newton-type methods.
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Report
(4 results)
Research Products
(26 results)
