Strong Convergence of Tikhonov Regularization Method for Solving Ill-Posed Problems in Hilbert Spaces

Abstract

It is well-known that solving ill-posed problems numerically without using methods for regularization is difficult because any small change in the data implies to large and random errors in the solution. We restrict the attention to Tikhonov regularization method where the original ill-posed problem is replaced with finding solution to a stable convex optimization problem which is called a regularized solution. This research aims to determine the convenient choice of the regularization parameter in order to establish the strong convergence.