A Regularization Procedure for Σn−i=1fi(zj)xi =g(zj), (j = 1, 2, …,n)

Abstract

A regularization procedure for linear systems of the type fi(zj)xi = g(zj), (j = 1, 2, …, n) is presented, which is particularly useful in the case when z1, z2, …, zn are close to each other. The associated numerical algorithm was tested on several examples for which analytic solutions do exist and was found to yield highly accurate results.