Computational Experiments On Ill-Conditioned Linear Systems by Regularization Technique

In this paper we consider ill-conditioned overdetermined linear systems Ax ¼ b where A and b are both contaminated by noise. This kind of problems are frequently arisingin discreetization of certain integral equations. First we present the total least square approach to ¯nd the closest system to the original one which is feasible. Then we presenttwo Computationally e±cient algorithms to solve the resulting fractional minimization problem. Finally, extensive numerical experiments are reported.