On approximating the solutions of nonlinear equations by a method of Aitken-Steffensen type - Adrian Diaconu (Journal of Numerical Analysis and Approximation Theory, 2014)
This paper completes the results that are presented in [14]. Using as a starting point the abstract method of the chord, in the mentioned paper we have presented an iterative method of approximation for the solutions of an equation. This method uses auxiliary sequences, and aims to improve the convergence order. The used method generalizes the method of Aitken-Steffensen. In the paper [14] we have given the statement of the main theorem and the statement and the proof of an auxiliary proposition concerning the convergence of some recurrence sequences of real numbers. In the present paper we give the proof of the main result and at the same time we discuss an interesting special case.