A modification of the numerical integration error method for the zero-finding problem of an analytic function

Abstract

The numerical integration error method (NIEM) is a zero-finding method which is based on the numerical evaluation of integrals of ƒ′/ƒ NIEM is an iterative method of higher-order, and (therefore) a lot of computational complexities are required. Besides it is necessary to select one from a number of choices of NIEM correction. In this paper we introduce an algorithm that improves computational efficiency of NIEM, yielding better results for the case of multiple or clustered zeros. Some numerical examples demonstrating the efficiency of this algorithm are introduced.