Name
Title | ||
|---|---|---|
A regularization framework for mildly ill-posed problems connected with pseudo-differential operator. |
Abstract | ||
|---|---|---|
Recently filter-based regularization methods have been well investigated for ill-posed problems when the forward operators are compact. There are many ill-posed problems connected with pseudo-differential operators. But there is no uniform method for this kind of problems. The work on generalization of filter-based regularization methods to pseudo-differential operator is necessary. In this paper, we present a regularization framework for solving the mildly ill-posed problems involved pseudo-differential operators. A general regularization method for this kind of problems is given. The order-optimal error estimates are derived under the usual source conditions. As an example, a new fractional Tikhonov regularization method could be cast into the general framework. Numerical experiments are conducted for showing the validity of the new fractional Tikhonov method. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.cam.2018.03.009 | Journal of Computational and Applied Mathematics |
Keywords | Field | DocType |
65R35,53C35,22E46 | Tikhonov regularization,Applied mathematics,Mathematical optimization,Well-posed problem,Pseudo-differential operator,Regularization (mathematics),Operator (computer programming),Mathematics | Journal |
Volume | ISSN | Citations |
341 | 0377-0427 | 0 |
PageRank | References | Authors |
0.34 | 4 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiang-Tuan Xiong | 1 | 77 | 20.18 |
| E. Zhuang | 2 | 0 | 0.34 |
| Xuemin Xue | 3 | 0 | 1.01 |
| Zhi Qian | 4 | 41 | 7.81 |