Multipoint Algorithms Arising from Optimal in the Sense of Kung-Traub Iterative Procedures for Numerical Solution of Nonlinear Equations

In this paper we will examine self-accelerating in terms of convergence speed and the corresponding index of effciency in the sense of Ostrowski - Traub of certain standard and most commonly used in practice multipoint iterative methods using several initial approximations for numerical solution of nonlinear equations (method regula falsi, modifications of Euler - Chebyshev method, Halley method, and others) due to optimal in the sense of the Kung-Traub algorithm of order 4 and 8. Some hypothetical iterative procedures generated by algorithms from order of convergence 16 and 32 are also studied (the receipt and publication of which is a matter of time, having in mind the increased interest in such optimal algorithms). The corresponding model theorems for their convergence speed and effciency index have been formulated and proved