Resumen de High order accelerating method for quadratic sequences
Rodrigo Castro Marín, Oscar A. Restrepo, Luis Echeverri
Aitken’s method is usually used for accelerating sequences with linear convergence.However, with sequences of order 2 it is not clear that this method accelerate them. In this paper, we are going to suppose that {pn}∞ n=0 is a sequence on R of order 2 and we want to accelerate it. Here, we prove that Aiken’s method decelerate such sequences. Therefore, we propose a new method for accelerating such a kind of sequences. As a corollary, we show that for quadratically convergent sequences {pn}∞ n=0, produced by a function G i.e., pn+1 = G (pn), this acceleration allows us to find methods of order of convergence 5. In particular, if the sequence is produced by the Newton’s Method, we obtain a method with convergence order 5 and efficiency index 4 √ 5 ≈ 1. 4953. Numerical examples with arbitrary precision are provided where especial cases are considered.
