Monte-Carlo Approach to Choose the Tikhonov Regularization Parameter for Solving Integral Equations

In this paper, we consider the numerical solution of Fredholm integral equations of the first kind. For solving this equations,following Tikhonov, we find regularization Parameter. This parameter acts as a smoothing filter of data used in a ill-posed problem. In general the numerical methods for finding this parameter lead to a linear or non linear problem with a free parameter. Here, we use Monte-Carlo approach in a interval to finding this parameter. For showing efficiency of method, we test our algorithm by comparing numerical results with the exact solution in ill-posed problems

Keywords:

First kind integral equation , Ill-posed Problem , Monte-Carlo method , Regularization parameter , Inverse problems