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Hofmann, Bernd; Mathé, Peter; Pereverzev, Sergei V. : Regularization by projection: Approximation theoretic aspects and distance functions

Hofmann, Bernd ; Mathé, Peter ; Pereverzev, Sergei V. : Regularization by projection: Approximation theoretic aspects and distance functions

Author(s):
Hofmann, Bernd
Mathé, Peter
Pereverzev, Sergei V.
Title:
Regularization by projection: Approximation theoretic aspects and distance functions
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 10, 2007
Mathematics Subject Classification:
65J20 [ Improperly posed problems; regularization ]
47A52 [ Ill-posed problems, regularization ]
47J06 [ Nonlinear ill-posed problems ]
47J25 [ Methods for solving nonlinear operator equations ]
Abstract:
The authors study regularization of non-linear inverse problems by projection methods. Non-linearity is controlled by some range invariance assumption. Emphasis is on approximation theoretic properties of the discretization which determine the convergence rates. Instead of using source conditions for the true solution to represent the error, the authors show how distance functions with respect to some benchmark smoothness are able to replace this. Some examples indicate how the results can be applied.
Keywords:
Non-linear ill-posed problems, regularization by discretization, Jackson- and Bernstein-type inequalities, convergence rates, fixed-point iteration, balancing principle, error estimates, distance functions, range inclusions
Language:
English
Publication time:
3 / 2007