Analytical and numerical studies of the convergence behavior of the \({\mathcal J}\) transformation

DOI10.1016/0377-0427(95)00022-4zbMath0854.65003OpenAlexW2120051911MaRDI QIDQ1919464

Herbert H. H. Homeier

Publication date: 23 July 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(95)00022-4

zbMATH Keywords

numerical resultsconvergence accelerationextrapolationsummation of divergent series\(E\)-algorithm\(J\)-transformationLevin transformations

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Extrapolation to the limit, deferred corrections (65B05) Numerical summation of series (65B10)

Related Items

A hierarchically consistent, iterative sequence transformation, Mathematical properties of a new Levin-type sequence transformation introduced by Čı́žek, Zamastil, and Skála. I. Algebraic theory, On condition numbers of the Shanks transformation, Convergence acceleration of logarithmically convergent series avoiding summation, Transforming logarithmic to linear convergence by interpolation, An asymptotically hierarchy-consistent, iterative sequence transformation for convergence acceleration of Fourier series, Scalar Levin-type sequence transformations, Numerical evaluation of Hilbert transforms for oscillatory functions: A convergence accelerator approach

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Interpolation between sequence transformations
• Sequence transformations and their applications
• A general extrapolation algorithm
• A new method for deriving Padé approximants for some hypergeometric functions
• Extrapolation of asymptotic expansions by a modified Aitken \(delta^ 2- \)formula
• Extrapolation methods theory and practice
• A hierarchically consistent, iterative sequence transformation
• Rational approximations for the modified Bessel function of the second kind
• Convergence speeding, convergence and summability
• An Algorithm for a Generalization of the Richardson Extrapolation Process
• Summing a common type of slowly convergent series of positive terms
• 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
• Brève communication. Transformations de suites
• Development of non-linear transformations for improving convergence of sequences
• A formula for accelerating the convergence of a general series
• On a Device for Computing the e m (S n ) Transformation