Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

Details Global Saturation of Regularization Methods for Inverse Ill-Posed Problems Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

2010-07-28

arxiv.org/abs/1008.0108v1

J Optim Theory Appl (2011) 148: 164-196

Mathematics

Functional Analysis

29 pages

Scientific paper

10.1007/s10957-010-9739-5

In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introduced by A. Neubauer in 1994. Necessary and sufficient conditions for a regularization method to have global saturation are provided. It is shown that for a method to have global saturation the total error must be optimal in two senses, namely as optimal order of convergence over a certain set which at the same time, must be optimal (in a very precise sense) with respect to the error. Finally, two converse results are proved and the theory is applied to find sufficient conditions which ensure the existence of global saturation for spectral methods with classical qualification of finite positive order and for methods with maximal qualification. Finally, several examples of regularization methods possessing global saturation are shown.

Affiliated with

Also associated with

No associations

Rating

Global Saturation of Regularization Methods for Inverse Ill-Posed Problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Global Saturation of Regularization Methods for Inverse Ill-Posed Problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Global Saturation of Regularization Methods for Inverse Ill-Posed Problems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-74968