Optimality of the Extended Inverse Interpolation Method for Solving Nonlinear Scalar Equations

Abstract

Abstract. The extended inverse interpolation method, developed by the author, is suitable for solving nonlinear scalar equations by fixed length multiple precision arithmetics. The method is free from derivative evaluations of the inverse function, and attempts to gain high efficiency by keeping and using all the information from the previous steps until convergence. The purpose of this paper is to show that the method is most efficient, compared with the extended inverse interpolation methods with derivative evaluations.