22-24 September 2021
Alpen-Adria-Universität Klagenfurt
Europe/Vienna timezone

Regularization as an approximation problem

24 Sep 2021, 11:20
30m
HS 1 (Alpen-Adria-Universität Klagenfurt)

HS 1

Alpen-Adria-Universität Klagenfurt

Speaker

Daniel Gerth

Description

Classically, regularization methods are often divided into three frameworks: variational regularization, iterative regularization, and regularization by projection. In this talk we consider regularization as an approximation problem in the classical Hilbert space setting. This enables us to treat all three categories in the same framework which we demonstrate on Tikhonov regularization and Landweber iteration. Our approach provides new insight on the way regularization works, helps understanding parameter choice rules, naturally includes discrete (finite dimensional) problems and, maybe most importantly, yields a numerically observable and computable quantity, namely a source element for the regularized solutions, that contains information about the smoothness of the unknown solution and the noise.

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