On remainder estimates for Levin-type sequence transformations

DOI10.1016/0010-4655(95)00103-MzbMath0908.65002OpenAlexW2032199336MaRDI QIDQ1269371

Herbert H. H. Homeier, Ernst Joachim Weniger

Publication date: 18 March 1999

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

Full work available at URL: https://doi.org/10.1016/0010-4655(95)00103-m

zbMATH Keywords

convergence accelerationiterative algorithmsextrapolationWeniger transformationKummer transformationnonlinear sequence transformationsremainder estimates\(I\) transformationLevin-type sequence transformations

Mathematics Subject Classification ID

Extrapolation to the limit, deferred corrections (65B05) Numerical summation of series (65B10)

Related Items (14)

Mathematical properties of a new Levin-type sequence transformation introduced by Čı́žek, Zamastil, and Skála. I. Algebraic theory ⋮ Global approximation for some functions ⋮ Convergence acceleration of alternating series ⋮ A comparative study of numerical steepest descent, extrapolation, and sequence transformation methods in computing semi-infinite integrals ⋮ Introduction to the determinantal formulae for the Levin-type algorithms ⋮ Convergence acceleration via combined nonlinear-condensation transformations ⋮ Irregular input data in convergence acceleration and summation processes: General considerations and some special Gaussian hypergeometric series as model problems ⋮ Extended procedures for extrapolation to the limit ⋮ Prediction of unknown terms of a sequence and its application to some physical problems ⋮ Multivariate approximants with levin-like transforms ⋮ A class of new transforms tailored for the hypergeometric series ⋮ Convergence acceleration of logarithmically convergent series avoiding summation ⋮ Scalar Levin-type sequence transformations ⋮ 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
• A general extrapolation algorithm
• Extrapolation of asymptotic expansions by a modified Aitken \(delta^ 2- \)formula
• A hierarchically consistent, iterative sequence transformation
• Extrapolation methods
• Rational approximations for the modified Bessel function of the second kind
• The three-dimensional convolution of reduced Bessel functions and other functions of physical interest
• Generalized neville type extrapolation schemes
• Acceleration of Linear and Logarithmic Convergence
• The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic, and octic anharmonic oscillators using nonlinear sequence transformations
• A Convergence Acceleration Method for Some Logarithmically Convergent Sequences
• Development of non-linear transformations for improving convergence of sequences
• Generating Functions for Bessel and Related Polynomials
• On a Device for Computing the e m (S n ) Transformation

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