| Title:
|
A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates (English) |
| Author:
|
Scherzer, Otmar |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
38 |
| Issue:
|
6 |
| Year:
|
1993 |
| Pages:
|
479-487 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a derivation of an a-posteriori strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems, which leads to optimal convergence rates. This strategy requires a special stability estimate for the regularized solutions. A new proof fot this stability estimate is given. (English) |
| Keyword:
|
nonlinear inverse problems |
| Keyword:
|
parameter choice strategy |
| Keyword:
|
nonlinear ill- posed problems |
| Keyword:
|
Hilbert spaces |
| Keyword:
|
Tikhonov regularization |
| Keyword:
|
convergence rate |
| Keyword:
|
numerical examples |
| MSC:
|
35R30 |
| MSC:
|
47H15 |
| MSC:
|
47J25 |
| MSC:
|
65F15 |
| MSC:
|
65J15 |
| MSC:
|
65J20 |
| MSC:
|
65M30 |
| idZBL:
|
Zbl 0797.65048 |
| idMR:
|
MR1241451 |
| DOI:
|
10.21136/AM.1993.104570 |
| . |
| Date available:
|
2008-05-20T18:46:39Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104570 |
| . |
| Reference:
|
[1] H. W. Engl H. Gfrerer: A posteriori parameter choice for general regularization methods for solving linear ill-posed problems.Appl. Num. Math. 4 (1988), 395-417. MR 0948506, 10.1016/0168-9274(88)90017-7 |
| Reference:
|
[2] H. W. Engl K. Kunisch A. Neubauer: Convergence rates for Tikhonov regularization of nonlinears ill-posed problems.Inverse Problems 5 (1989), 523-540. MR 1009037 |
| Reference:
|
[3] H. Gfrerer: An a-posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates.Mathematics of Computation 49 (1987), 507-522. Zbl 0631.65057, MR 0906185, 10.1090/S0025-5718-1987-0906185-4 |
| Reference:
|
[4] C. W. Groetsch: The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind.Pitman, Boston, 1984. Zbl 0545.65034, MR 0742928 |
| Reference:
|
[5] A. Neubauer: Tikhonov regularization for non-linear ill-posed problems: optimal convergence rates and finite-dimensional approximation.Inverse Problems 5 (1989), 541-557. MR 1009038 |
| Reference:
|
[6] O. Scherzer H. W. Engl K. Kunisch: Optimal a-posteriori parameter choice for Tikhonov regularization for solving nonlinear ill-posed problems.SIAM J. on Numer. Anal., to appear. MR 1249043 |
| Reference:
|
[7] T. L Seidman C. R. Vogel: Well-posedness and convergence of some regularization methods for nonlinear ill-posed problems.Inverse Problems 5 (1989), 227-238. MR 0991919 |
| . |
