Name
Abstract | ||
|---|---|---|
Although the residual method, or constrained regularization, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov regularization, where a series of new results for regularization in Banach spaces has been published in the recent years. The present paper intends to bridge the gap between the existing theories as far as possible. We develop a stability and convergence theory for the residual method in general topological spaces. In addition, we prove convergence rates in terms of (generalized) Bregman distances, which can also be applied to non-convex regularization functionals. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.amc.2011.08.009 | Applied Mathematics and Computation |
Keywords | Field | DocType |
Ill-posed problems,Regularization,Residual method,Sparsity,Stability,Convergence rates | Tikhonov regularization,Residual,Mathematical optimization,Well-posed problem,Mathematical analysis,Backus–Gilbert method,Regularization (mathematics),Proximal gradient methods for learning,Zeta function regularization,Mathematics,Regularization perspectives on support vector machines | Journal |
Volume | Issue | ISSN |
218 | 6 | 0096-3003 |
Citations | PageRank | References |
6 | 0.62 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Markus Grasmair | 1 | 37 | 4.61 |
| Markus Haltmeier | 2 | 74 | 14.16 |
| Otmar Scherzer | 3 | 346 | 52.10 |