Optimal Parameterised Families of Modified Householder’s Method with and without Restraint on Function Derivative

This paper introduces two families of modified Householder’s method (HM) that are optimal in line with Kung-Traub conjecture given in [4]. The modification techniques employed involved approximation of the function derivatives in the HM with divided difference operator, a polynomial function approximation and the modified Wu function approximation in [17]. These informed the formation of two families of methods that that are optimal and do not or require function derivative evaluation. The both families do not breakdown when f(·) ≈ 0 as in the case with the HM and many existing modified HM. From the convergence investigation carried out on the methods, the sequence of approximations produced by the methods, converged to solution of nonlinear equation with order four. The implementation of the methods was illustrated and numerical results obtained were compared with that of some recently developed methods.