Asymptotic behaviour of iterated modified \(\Delta^ 2\) and \(\theta_ 2\) transforms on some slowly convergent sequences

DOI10.1007/BF02141947zbMath0784.65003MaRDI QIDQ688140

Paul Sablonniere

Publication date: 6 December 1993

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

zbMATH Keywords

convergence accelerationasymptotic behaviourAitken's delta-square transformiterated Lubkin's transform

Mathematics Subject Classification ID

Extrapolation to the limit, deferred corrections (65B05)

Related Items

A convergence and stability study of the iterated Lubkin transformation and the $\theta$-algorithm, Acceleration of convergence of some infinite sequences \(\{A_n\}\) whose asymptotic expansions involve fractional powers of \(n\) via the \(\widetilde{d}^{(m)}\) transformation, Comparison of four nonlinear transforms on some classes of logarithmic fixed point sequences, Interpolation and convergence of Bernstein-Bézier coefficients, 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

Cites Work

• Convergence acceleration of some logarithmic sequences
• Convergence acceleration of logarithmic fixed point sequences
• Extrapolation of asymptotic expansions by a modified Aitken \(delta^ 2- \)formula
• Comparison of four algorithms accelerating the convergence of a subset of logarithmic fixed point sequences
• Summing a common type of slowly convergent series of positive terms
• A Convergence Acceleration Method for Some Logarithmically Convergent Sequences