| Project/Area Number |
11440025
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The University of Tokyo |
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Principal Investigator |
YAMAMOTO Masahiro School of Math. Sci., The University of Tokyo, Prof., 大学院・数理科学研究科, 助教授 (50182647)
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| Co-Investigator(Kenkyū-buntansha) |
USHIJIMA Teruo The University of Electro-Communications, Dept. Comp. Sci., Professor, 電気通信学部, 教授 (10012410)
SAITOH Saburo Gunma University, Faculty of Engineering, Professor, 工学部, 教授 (10110397)
KAWARADA Hideo Chiba University, Faculty of Engineering, Professor, 工学部, 教授 (90010793)
MIYOSHI Tetsuhiko Yamaguchi University, Dept. of Math. Sci., Professor, 理学部, 教授 (60040101)
KAKO Takashi The University of Electro-Communications, Dept. Comp. Sci., Professor, 電気通信学部, 教授 (30012488)
久保 雅義 京都大学, 情報学, 講師 (10273616)
磯 祐介 京都大学, 情報学, 教授 (70203065)
大西 和榮 茨城大学, 理学部, 教授 (20078554)
登坂 宣好 日本大学, 生産工学部, 教授 (00059776)
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| Project Period (FY) |
1999 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥11,800,000 (Direct Cost: ¥11,800,000)
Fiscal Year 2001: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2000: ¥4,100,000 (Direct Cost: ¥4,100,000)
Fiscal Year 1999: ¥4,900,000 (Direct Cost: ¥4,900,000)
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| Keywords | stability / inverse problem / impedance tomography / free boundary problem / finite element / multile precision / Kalman filter / 多倍長計算 / 幾何形状決定 / 係数決定 / インピーダンス・トモグラフィ |
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| Research Abstract |
This project aims at mathematical analysis and numerical analysis based on the mathematical analysis for inverse problems in applied sciences, Moreover we have studied related problems in applications, from the viewpoint of inverse problems, and prepared possible numerical methods.
We conclude that by this project, we have established satisfactory theoretical results. Moreover, as for the development of numerical methods on the basis of the theoretical aspects, several methods have been proposed and tested for numerical examples. Still we have not compared the numerical results with real data directly from the real worlds such as works or plants. Therefore the continuation of this kind of projects are strongly demanded.
For researches of related problems with inverse problems, the participants have achieved remarkable results by their own specialities.
We have held several surveys concerning inverse problems by foreign researchers and taken part in international conferences on inverse problems for presenting the outputs of this project.
With results obtained by this project, M. Yamamoto et al. have published a monograph on the mathematics and the numerical methods of inverse problems.
Onishi, Tosaka, Iso, Kawarada, Miyoshi, Kimura, Ushijima and Kako have worked for inverse problems and related problems in applied sciences, from numerical points of view. Nakamura, Saitoh, Ikehata, Tanuma, Kubo have worked for theoretical aspects of inverse problems.
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