Convergence acceleration of logarithmic fixed point sequences

DOI10.1016/0377-0427(87)90171-3zbMath0622.65002OpenAlexW2008134816MaRDI QIDQ1091072

Paul Sablonniere

Publication date: 1987

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(87)90171-3

zbMATH Keywords

convergence accelerationsuperconvergenceasymptotic expansionsdelta square algorithmlogarithmic fixed point sequenceslogarithmical convergencetheta two algorithm

Mathematics Subject Classification ID

Extrapolation to the limit, deferred corrections (65B05)

Related Items (11)

Acceleration of some logarithmic sequences ⋮ 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 ⋮ Comparison of four algorithms accelerating the convergence of a subset of logarithmic fixed point sequences ⋮ 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 ⋮ A simultaneous process for convergence acceleration and error control ⋮ Convergence acceleration of some logarithmic sequences ⋮ Prediction proberties of Aitken's iterated \(\Delta^2\) process, of Wynn's epsilon algorithm, and of Brezinski's iterated theta algorithm

Cites Work

• Sequence transformations and their applications
• Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series
• Accélération de la convergence en analyse numérique
• Numerical Comparisons of Nonlinear Convergence Accelerators
• The Set of Logarithmically Convergent Sequences Cannot be Accelerated
• Acceleration of Linear and Logarithmic Convergence
• Development of non-linear transformations for improving convergence of sequences
• Numerical Quadrature and Asymptotic Expansions
• Survey of Extrapolation Processes in Numerical Analysis
• Numerical Quadrature by the ε-Algorithm
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