A unified approach for regularizing discretized linear ill‐posed problems

Abstract

In this paper we deal with regularization approaches for discretized linear ill‐posed problems in Hilbert spaces. As opposite to other contributions concerning this topic the smoothness of the unknown solution is measured with so‐called approximative source conditions. This idea allows us to generalize known convergence rates results to arbitrary classes of smoothness conditions including logarithmic and general source conditions. The considerations include an a‐posteriori parameter choice strategy for the regularization parameter and the discretization level. Results of one numerical example are presented.

Key words:

• inverse problem
• linear ill‐posed problem,regularization
• projection method
• convergence rates