ARIES: A Computer Program for the Solution of First Kind Integral Equations with Noisy Data

摘要

The method of regularization using a weighted Sobolev norm is developed and applied for the numerical solution of first kind integral equations with noisy data. The algorithm and computer program described in this report are based on the singular value decomposition (SVD) of the discretized least squares functional. The method of cross validation is developed for choosing the regularization parameter and its relationship to the SVD is described. Some example problems are included to give the reader a feel for the delicacy of ill-posed problems. They include finding the first and second derivatives of functions given by data that are noisy and solving an inverse heat conduction problem. (ERA citation 09:007070)