The balancing principle in solving semi-discrete inverse problems in Sobolev scales by Tikhonov method

Abstract

In this article we discuss a regularization of semi-discrete ill-posed problem appearing as a result of application of a collocation method to Fredholm integral equation of the first kind. In this context we analyse Tikhonov regularization in Sobolev scales and prove error bounds under general source conditions. Moreover, we study an a posteriori regularization parameter choice by means of the balancing principle.

Keywords:

• inverse problems in Sobolev scales
• Tikhonov regularization
• collocation method
• a posteriori parameter choice
• error bound

AMS Subject Classifications::

• 47A52
• 45Q05
• 46E22
• 45A05

Acknowledgements

This study has been performed when Sergei G. Solodky visited Johann Radon Institute for Computational and Applied Mathematics. This visit was possible due to the cooperation agreement between Austrian Academy of Sciences and National Academy of Sciences of Ukraine. Sergei G. Solodky wants to express his gratitude for the excellent conditions and hospitality.