The external aggregation Newton's method for solving nonlinear equations and applications

Abstract

Different modified Newton’s methods are widely used in modern computational engineering science, applied mechanics, economics, optimization problems and other disciplines. On the other hand aggregation of information takes a significant place in many knowledge-based systems, where aggregation of data or values is needed. In this paper we theoretically analysed a new modification of Newton’s method based on aggregation function applied on finding multiple roots of nonlinear equations, and numerically verified theoretical results on the examples with simple and multiple roots. Numerical analysis of the proposed approach with obtained results and the related discussion are presented on examples in practice.