2006 Fiscal Year Final Research Report Summary
Research of the applications of the theory of reproducing kernels
| Project/Area Number |
16540137
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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 |
Basic analysis
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| Research Institution | Gunma University |
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Principal Investigator |
SAITOH Saburou GUNMA UNIVERSITY, Department of Mathematics, Faculty of Engineering, Professor, 工学部, 教授 (10110397)
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| Co-Investigator(Kenkyū-buntansha) |
IKEHATA Masaru GUNMA UNIVERSITY, Department of Mathematics, Faculty of Engineering, Professor, 工学部, 教授 (90202910)
AMANO Kazuo GUNMA UNIVERSITY, Department of Mathematics, Faculty of Engineering, Professor, 工学部, 助教授 (90137795)
TNUMA Kazumi GUNMA UNIVERSITY, Department of Mathematics, Faculty of Engineering, Associated Professor, 工学部, 助教授 (60217156)
AMOU Masaaki GUNMA UNIVERSITY, Department of Mathematics, Faculty of Engineering, Associated Professor, 工学部, 助教授 (60201901)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Reproducing kernels / Tikhonov regularization / Numerical Analysis / Algorithm / Computer / Computer Graphic / Analysis / Applicable Analysis |
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| Research Abstract |
We established a general theory of the applications of the theory of reproducing kernels to the Tikhonov regularization and derived many concrete results in inverse problems as applications of the general theory. typical results are the effective inversion formulas for the heat conduction and the real inversion formula of the Laplace transform that are very famous ill-posed problems and are well-known as very difficult problems. We succeeded in their numerical analysis and showed the results in the computer graphics with our related collaborators-in particular, Professors Tsutomu Matuura and Hiroshi Fujiwara. Furthermore, we were able to publish their results in which are major international journals. We derived the concrete results in ordinary differential equations, the wave equation, Poisson equation, Dirichlet problem, and so on.
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Research Products
(38 results)
