New Third Order Nonlinear Solvers for Multiple Roots (uncorrected proof)

Abstract

Two third order methods for finding multiple zeros of nonlinear functions are developed. One method is based on Chebyshev’s third order scheme (for simple roots) and the other is a family based on a variant of Chebyshev’s which does not require the second derivative. Two other more efficient methods of lower order are also given. These last two methods are variants of Chebyshev’s and Osada’s schemes. The informational efficiency of the methods is discussed. All these methods require the knowledge of the multiplicity.