2016 Fiscal Year Final Research Report
Applications of Reproducing kernel theory and its new development in engineering and medical science
| Project/Area Number |
26400192
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Foundations of mathematics/Applied mathematics
|
|---|
| Research Institution | Gunma University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2014-04-01 – 2017-03-31
|
| Keywords | 再生核理論 / 逆問題 / 数値計算 / 正則化 / 積分方程式 / アルゴリズム / 離散化 |
|---|
| 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. Especially, we tried new approach to the field of medical science. Specifically, we published 2 papers and presented 3 papers in Medical Sciences (Microscopic Image of Podocyte and Cochlear cells) and we published 9 papers and presented 18 papers in Mathematical Sciences (general reproducing kernels and division by zero).
|
| Free Research Field |
数学，応用数理
|
