Some Thoughts on the Choice of Regularization Parameter of Ill-Posed Problems

Dr. James F. Epperson

Department of Mathematical Sciences
University of Alabama in Huntsville

October 3, 1997

Abstract

In order to numerically solve an ill-posed problem we need to "regularize" the original problem. This regularization introduces some additional error into the approximation and in this talk we will discuss and compare some of the methods used for determining the size of the regularization parameter. The conclusion is that an older method originating in the Soviet literature is perhaps superior to the more modern methods currently used. The talk is elementary in nature and should be accessible to graduate students without a lot of background.