Comparison of four algorithms accelerating the convergence of a subset of logarithmic fixed point sequences

DOI10.1007/BF02142320zbMath0749.65002OpenAlexW2067931111MaRDI QIDQ1186616

Paul Sablonniere

Publication date: 28 June 1992

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02142320

zbMATH Keywords

convergencenumerical examplesconvergence accelerationextrapolationcomparison of algorithmsepsilon-algorithmlogarithmic sequencesAitken's delta-square process\(W\)-transformtheta-two algorithm

Mathematics Subject Classification ID

Extrapolation to the limit, deferred corrections (65B05)

Related Items (10)

Asymptotic solutions of the translation equation ⋮ Correction to the paper: Asymptotic solutions of the translation equation ⋮ Comparison of four nonlinear transforms on some classes of logarithmic fixed point sequences ⋮ Vector sequence transformations for the acceleration of logarithmic convergence ⋮ Extrapolation methods for some singular fixed point sequences ⋮ Asymptotic behaviour of iterated modified \(\Delta^ 2\) and \(\theta_ 2\) transforms on some slowly convergent sequences ⋮ Irregular input data in convergence acceleration and summation processes: General considerations and some special Gaussian hypergeometric series as model problems ⋮ Construction of new generalizations of Wynn's epsilon and rho algorithm by solving finite difference equations in the transformation order ⋮ On the Computation of Nonhyperbolic Fixed Points ⋮ Prediction proberties of Aitken's iterated \(\Delta^2\) process, of Wynn's epsilon algorithm, and of Brezinski's iterated theta algorithm

Cites Work

• Convergence acceleration of some logarithmic sequences
• Sequence transformations and their applications
• Convergence acceleration of logarithmic fixed point sequences
• Extrapolation of asymptotic expansions by a modified Aitken \(delta^ 2- \)formula
• Convergence speeding, convergence and summability
• Numerical Comparisons of Nonlinear Convergence Accelerators
• The Set of Logarithmically Convergent Sequences Cannot be Accelerated
• Summing a common type of slowly convergent series of positive terms
• Acceleration of Linear and Logarithmic Convergence
• A Convergence Acceleration Method for Some Logarithmically Convergent Sequences
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