Modified chain least squares method and some numerical results

Abstract

Recently, in order to increase the efficiency of least squares method in numerical solution of ill-posed problems, the chain least squares method is presented in a recurrent process by Babolian et al. Despite the fact that the given method has many advantages in terms of accuracy and stability, it does not have any stopping criterion and has high computational cost. In this article, the attempt is to decrease the computational cost of chain least squares method by introducing the modified least squares method based on stopping criterion. Numerical results show that the modified method has high accuracy and stability and because of its low computational cost, it can be considered as an efficient numerical method.