Construction of optimal order nonlinear solvers using inverse interpolation

Abstract

There is a vast literature on finding simple roots of nonlinear equations by iterative meth- ods. These methods can be classified by order, by the information used or by efficiency. There are very few optimal methods, that is methods of order 2m requiring m + 1 function evaluations per iteration. Here we give a general way to construct such methods by using inverse interpolation and any optimal two-point method. The presented optimal multi- point methods are tested on numerical examples and compared to existing methods of the same order of convergence.