摘要：In this work, we derive a one-parameter family ofSuper Halley’s method for finding simple roots of nonlinearequations. The scheme is powerful since it regenerates aninfinity interesting methods. The convergence analysis showsthat the order of convergence of each method of the proposedfamily is at least three. The originality of the new familymanifests in the fact that all these methods are governed by arecurring formula that depends on a natural integer parameterp. Moreover, under certain conditions, the convergence speedof these methods improves by increasing p. A fairly detailedstudy on their global convergence is carried out. To illustratethe abilities and performances of proposed family, numericalcomparisons have been made with several other existing thirdorder and higher order methods.
关键词：Nonlinear equations; One-parameter family; Iterative methods; Order of convergence; Third order method; Super Halley’s method
