2014 Fiscal Year Final Research Report
Applications of Reproducing kernel theory and its new development in engineering
| Project/Area Number |
23540121
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Gunma University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
SAITOH Saburou 群馬大学, 名誉教授 (10110397)
|
|---|
| Project Period (FY) |
2011-04-28 – 2015-03-31
|
| Keywords | 再生核 / 逆問題 / 離散化 / 正則化 / 積分変換 / アルゴリズム / 数値計算 |
|---|
| Outline of Final Research Achievements |
We developed a new type of Tikhonov 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 constructed concrete algorithms for solving those problems and confirmed their effectiveness by numerical experiments.
In practice, we have studied the following problems: 1) explicit solution of inverse problem in wave equation, 2) solution of Dirichlet problem with arbitrary boundary shape, 3) new discretization method for solving regularized integral equation, 4) method for separating and extracting mixed signal with complex Gabor wavelet transform, 5) validity of our algorithm for constructing of approximate solution of Poisson equation, 6) expansion of reproducing kernel space for inverse problem of heat conduction.
|
| Free Research Field |
数理工学
|
