2010 Fiscal Year Final Research Report
Applications of the reproducing kernel theory to inverse problems and their engineering approach
| Project/Area Number |
20540105
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Gunma University |
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Principal Investigator |
MATSUURA Tsutomu Gunma University, 大学院・工学研究科, 准教授 (80181692)
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| Co-Investigator(Kenkyū-buntansha) |
SAITOH Saburou 群馬大学, 名誉教授 (10110397)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 逆問題 / 再生核理論 / ラプラス実逆変換 / 正則化 |
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| Research Abstract |
We developed a new type of Thihonov regularization combined with the theory of reproducing kernels. Using our method of regularization we have challenged some famous and historically difficult inverse problems. Furthermore we designed concrete algorithms for solving those problems. In particular we studied real inversion of Laplace transform, solving method by singular value decomposition, representation of inverse transform of nonlinear mapping and separation of mixed signals. In addition for engineer in the field we filed a patent application of our algorithm for inversion of Laplace transform.
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