Multiplicative Newton’s Methods with Cubic Convergence

Abstract

In this paper, we develop some modifications of the multiplicative Newton method which are third-order convergence. We use the multiplicative Newton Theorem and Newton Cotes quadrature formulas to present these new modifications of the multiplicative Newton method. Using the multiplicative Taylor expansion, we give also the convergence analysis of these new methods. Furthermore, we compare the multiplicative Newton methods with the classical Newton methods in details.