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 efficiency 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 efficiency index have been formulated and proved. 46 Boryana Ignatova et al.

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