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Development of the levin-type algorithms for accelerating convergence of sequences

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2006年第2期64卷 229-241页

作者： Thukral, R Pade Res Ctr Leeds LS17 5JS W Yorkshire England

There are two aims of this paper. Firstly we shall introduce the determinantal representations of the new levin-type algorithms and secondly we shall demonstrate further development of the levin-type algorithms. We consider the use of the levin-type algorithms to accelerate the convergence of scalar sequence and their effectiveness for approximating the solution of a given power series is illustrated. In process we shall demonstrate the convergence of each of the methods considered. The approximate solution of the super enhanced levin algorithm and the efficient levin algorithm are found to be substantially more accurate than the Cizek, Zamastil and Skala transformation and the iterated Aitken Delta(2) algorithm. (c) 2005 Published by Elsevier Ltd.

关键词： levin-type algorithms iterated Aitken Delta(2) algorithm Cizek, Zamastil and Skala transformation convergence acceleration

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Introduction to the determinantal formulae for the levin-type algorithms

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期181卷 516-526页

作者： Thukral, R. Pade Res Ctr Leeds LS17 5JS W Yorkshire England

There are two aims of this paper. Firstly, we shall introduce the determinantal formulae for the new levin-type algorithms and secondly we shall demonstrate the similarities between the new levin-type algorithms and the well established methods, namely, the Aitken Delta(2) algorithm, the Brezinski theta algorithm and the Lubkin transformation. Actually, there are two groups of similarities. First of the group demonstrates the similarity between the super enhanced levin algorithm, the super modified levin algorithm, the Brezinski theta algorithm and the Lubkin transformation. The second group of similarity is between the modified levin algorithm, the original levin transformation and the Aitken Delta(2) algorithm. (c) 2006 Published by Elsevier Inc.

关键词： levin-type algorithms Brezinski theta algorithm Lubkin transformation acceleration convergence Aitken Delta 2 algorithm classical levin transformation

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