On adaptive discretization schemes for the solution of ill-posed problems with semiiterative methods

Abstract

In this paper, we investigate an adaptive discretization strategy for ill-posed linear problems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a stopping criterion as the discrepancy principle or the balancing principle yields an order optimal regularization scheme and allows to reduce the computational costs.

Keywords:

• linear ill-posed problem
• semiiterative method
• discrepancy principle
• balancing principle
• Hölder-type source condition
• adaptive discretization scheme

AMS Subject Classifications:

• 65F10
• 65J20
• 47A52

Notes

This work was supported by Marie Curie Actions – International Research Staff Exchange Scheme (IRSES) FP7-People-2011 [IRSES Project number 295164].