We describe a new method for accelerating the convergence of scalar sequence. We express the new method as a rational fraction, namely the rational approximant. The effectiveness of the new method is compared with the...
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We describe a new method for accelerating the convergence of scalar sequence. We express the new method as a rational fraction, namely the rational approximant. The effectiveness of the new method is compared with the well established methods namely, the Lubkin transformation, the iterated Aitken Delta(2) algorithm, the Levin transformation, the Epsilon algorithm and the brezinski theta algorithm for approximating the partial sum of a given alternating series. Estimates of the partial sum produced by the new rational approximant method are found to be substantially more accurate than the classical methods. (c) 2006 Elsevier Inc. All rights reserved.
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 t...
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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.
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