Irregular input data in convergence acceleration and summation processes: General considerations and some special Gaussian hypergeometric series as model problems

DOI10.1016/S0010-4655(00)00175-2zbMath0976.65006arXivmath/0003227OpenAlexW1972234900MaRDI QIDQ5934218

Ernst Joachim Weniger

Publication date: 19 December 2001

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0003227

zbMATH Keywords

numerical examplesconvergence accelerationGaussian hypergeometric seriessequence transformationsummation processes

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Extrapolation to the limit, deferred corrections (65B05) Computation of special functions and constants, construction of tables (65D20) Numerical summation of series (65B10)

Related Items (9)

Mathematical properties of a new Levin-type sequence transformation introduced by Čı́žek, Zamastil, and Skála. I. Algebraic theory ⋮ Extrapolation methods for improving the convergence of oligomer calculations to the infinite chain limit of quasi-one-dimensional stereoregular polymers. ⋮ Introduction to the improved Levin-type algorithms for accelerating convergence of sequence. ⋮ Acceleration of generalized hypergeometric functions through precise remainder asymptotics ⋮ Introduction to the determinantal formulae for the Levin-type algorithms ⋮ Nonlinear sequence transformation-based continuous-time wavelet filter approximation ⋮ Generalizations of Aitken's process for a certain class of sequences ⋮ Development of the Levin-type algorithms for accelerating convergence of sequences ⋮ Convergence analysis of the summation of the factorially divergent Euler series by Padé approximants and the delta transformation

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