Comparison of four nonlinear transforms on some classes of logarithmic fixed point sequences

DOI10.1016/0377-0427(96)80013-6zbMath0840.65002OpenAlexW2016735054MaRDI QIDQ1903676

Paul Sablonniere

Publication date: 1 February 1996

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(96)80013-6

zbMATH Keywords

instabilitynumerical examplesconvergence accelerationerror propagationasymptotic error estimatesnonlinear sequence transformationslogarithmic fixed point sequencesLubkin's methodnonlinear recursive convergence acceleration algorithmsSteffenson's methods

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Extrapolation to the limit, deferred corrections (65B05)

Related Items (2)

Irregular input data in convergence acceleration and summation processes: General considerations and some special Gaussian hypergeometric series as model problems ⋮ Prediction proberties of Aitken's iterated \(\Delta^2\) process, of Wynn's epsilon algorithm, and of Brezinski's iterated theta algorithm

Uses Software

• NUMAL

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extrapolation methods for some singular fixed point sequences
• Particular rules for the \(\Theta\)-algorithm
• Asymptotic behaviour of iterated modified \(\Delta^ 2\) and \(\theta_ 2\) transforms on some slowly convergent sequences
• Interpolation between sequence transformations
• Acceleration methods based on convergence tests
• Accelerable subsets of logarithmic sequences
• 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
• Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series
• Comparison of four algorithms accelerating the convergence of a subset of logarithmic fixed point sequences
• Accélération de la convergence en analyse numérique
• Acceleration of some logarithmic sequences
• Convergence speeding, convergence and summability
• Automatic Selection of Sequence Transformations
• 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
• Convergence Properties of Some Nonlinear Sequence Transformations
• Acceleration of Linear and Logarithmic Convergence
• A Convergence Acceleration Method for Some Logarithmically Convergent Sequences
• Development of non-linear transformations for improving convergence of sequences

This page was built for publication: Comparison of four nonlinear transforms on some classes of logarithmic fixed point sequences