High order accelerating method for quadratic sequences
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[1] Universidad de Valparaíso
Universidad de Valparaíso
Valparaíso, Chile
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[2] Universidad de Antioquia
Universidad de Antioquia
Colombia
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- Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 81, Nº. 2, 2024, págs. 283-290
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
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.
