2013 Fiscal Year Final Research Report
New GMRES algorithm for solving large scale inverse problems on a cloud computing
| Project/Area Number |
23654040
|
|---|
| Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Keio University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
TANI Atsushi 慶應義塾大学, 理工学部, 名誉教授 (90118969)
OHNO Yoshio 慶應義塾大学, 理工学部, 名誉教授 (20051865)
YAMAMOTO Yoshikazu 慶應義塾大学, 理工学部, 旧教授 (20051873)
TAMURA Youzou 慶應義塾大学, 理工学部, 教授 (50171905)
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Keywords | 非適切な問題 / 離散型悪条件問題 / 逆問題 / GMRES / Krylov部分空間 / Tikhonov正則化 / 制約条件 / augmentation |
|---|
| Research Abstract |
GMRES regularization method is arguably the most popular solution for linear discrete ill-posed problems. We explores different regularization methods as a means of yielding stable solutions for linear discrete ill-posed problems.
The regularization with GMRES must be implemented in two stages, which are designed to generate an approximate solution of a linear system through the use of GMRES, and to determine the most appropriate solution by using a constraint. In the first stage, particular behaviors of GMRES and preconditioned GMRES for linear discrete ill-posed problems are identified. In the second stage, a simplified Tikhonov threshold as a constraint to determine the best approximate solution is explored. Numerical experiments have been tabulated to underline the effectiveness of our proposed method.
|
