Title

On weakly bounded noise in ill-posed problems

Authors

Authors

P. P. B. Eggermont; V. N. LaRiccia;M. Z. Nashed

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Inverse Probl.

Keywords

NONLINEAR TIKHONOV REGULARIZATION; HILBERT SCALES; INVERSE PROBLEMS; CONVERGENCE-RATES; EQUATIONS; PRINCIPLE; Mathematics, Applied; Physics, Mathematical

Abstract

We study compact operator equations with noisy data in Hilbert space. Instead of assuming that the error in the data converges strongly to zero, we only assume a type of weak convergence. Under the source conditions that are usually assumed in the presence of convex constraints, we derive optimal convergence rates for convexly constrained Phillips-Tikhonov regularization. We also discuss a version of the Lepskii method for selecting the regularization parameter.

Journal Title

Inverse Problems

Volume

25

Issue/Number

11

Publication Date

1-1-2009

Document Type

Article

DOI Link

http://dx.doi.org/10.1088/0266-5611/25/11/115018

Language

English

First Page

14

WOS Identifier

WOS:000271481500018

ISSN

0266-5611

Recommended Citation

"On weakly bounded noise in ill-posed problems" (2009). Faculty Bibliography 2000s. 1511.
https://stars.library.ucf.edu/facultybib2000/1511