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Let $(S_{n})$ be some vector sequence, converging to S, satisfying $S_{n} - S \sim ϱ^{n} n^{θ} (β_{0} + β_{1} n^{- 1} + β_{2} n^{- 2} + . . .), 0 | ϱ | 1, θ 0$ , where $β_{0} (\neq 0), β_{1}, . . .$ are constant vectors independent of n. The purpose of this paper is to provide acceleration methods for these vector sequences. Comparisons are made with some known algorithms. Numerical examples are also given.

Some fast finite-difference solvers for Dirichlet problems on general domains

Ta Van Dinh (1982)

Aplikace matematiky

The author proves the existence of the multi-parameter asymptotic error expansion to the five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on general domains. By Richardson extrapolation, this expansion leads to a simple process for accelerating the convergence of the method.

Some Generalizations of the Euler-Knopp Transformation.

J.N. Lyness, Bruno Gabutti (1986)

Numerische Mathematik

Some new formulas for $π$ .

Almkvist, Gert, Krattenthaler, Christian, Petersson, Joakim (2003)

Experimental Mathematics

Some remarks on $I$ -faster convergent infinite series

Ladislav Matejíčka (2009)

Mathematica Bohemica

A structure of terms of $I$ -faster convergent series is studied in the paper. Necessary and sufficient conditions for the existence of $I$ -faster convergent series with different types of their terms are proved. Some consequences are discussed.

Some results on convergence acceleration for the E-algorithm

A. Fdil (1997)

Applicationes Mathematicae

Some new results on convergence acceleration for the E-algorithm which is a general extrapolation method are obtained. A technique for avoiding numerical instability is proposed. Some applications are given. Theoretical results are illustrated by numerical experiments

Some results on nonlinear and nonlogarithmic sequences and their acceleration

M. D. Benchiboun (1991)

Applicationes Mathematicae

Spolehlivost numerických výpočtů

Michal Křížek, Milan Práger, Emil Vitásek (1997)

Pokroky matematiky, fyziky a astronomie

Stable Convergence Acceleration Using Laplace Transforms.

Sven-Ake Gustafson (1985)

Numerische Mathematik

Summation of series by some substitutions

Z. Cylkowski (1988)

Applicationes Mathematicae

Summation of slowly convergent series

Walter Gautschi (1994)

Banach Center Publications

Among the applications of orthogonal polynomials described briefly on my previous visit to this Center [9, §3.2] were slowly convergent series whose terms could be represented in terms of the Laplace transform at integer arguments. We proposed to sum such series by means of Gaussian quadrature rules applied to suitable integrals involving weight functions of Einstein and Fermi type (cf. [13]). In the meantime it transpired that the technique is applicable to a large class of numerical series and,...

Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method

Pengzhan Huang (2014)

Applications of Mathematics

This paper presents a superconvergence result based on projection method for stabilized finite element approximation of the Stokes eigenvalue problem. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The paper complements the work of Li et al. (2012), which establishes the superconvergence result of the Stokes equations by the stabilized finite element method. Moreover, numerical tests confirm the theoretical analysis.

Sur les développements en série des fonctions d'une seule variable.

Darboux, G. (1876)

Journal de Mathématiques Pures et Appliquées

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