摘要：In this work, we will present an important variantof Halley’s method for solving non-linear equations: ImprovedHalley’s method (IHM). Analysis of convergence shows thatthe proposed method is cubically convergent for a simple root.A fairly detailed study of its global convergence willperformed. We will prove that the proposed method is veryinteresting since, under certain conditions, it converges fasterthan Halley’s method, Super-Halley’s method and Chebyshev’smethod which are three of the best iterative techniques. Oncomparison with the sixth and eighth order methods, theybehave either similarly or better for the examples considered.
关键词：Global convergence; Halley’s method; Improved Halley’s iterative methods; Nonlinear equations; Rate of convergence; Third order method
