About Regularization of Severely Ill-Posed Problems by Standard Tikhonov's Method with the Balancing Principle

Abstract

In the present paper for a stable solution of severely ill-posed problems with perturbed input data, the standard Tikhonov method is applied, and the regularization parameter is chosen according to balancing principle. We establish that the approach provides the order of accuracy on the class of problems under consideration.

Keywords:

• severely ill-posed problems
• standard Tikhonov method
• balancing principle
• approximate accuracy

AMS Subject Classification:

• 47A52
• 65R30