Iterations of convergence accelerating nonlinear transforms

DOI10.1016/0010-4655(89)90030-1zbMath0798.65006OpenAlexW1966288246MaRDI QIDQ1330614

Ranjan Bhattacharya, Dhiranjan Roy, Siddhartha Bhowmick

Publication date: 30 October 1994

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

Full work available at URL: https://doi.org/10.1016/0010-4655(89)90030-1

zbMATH Keywords

algorithmstabilityiterationconvergence accelerationerror estimatealternating monotone and divergent seriesLevin \(u\) transformnonlinear transforms

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, On the regularity of the Levin \(u\)-transform, Rational approximants generated by the \(u\)-transform, Extrapolation methods for improving the convergence of oligomer calculations to the infinite chain limit of quasi-one-dimensional stereoregular polymers., Irregular input data in convergence acceleration and summation processes: General considerations and some special Gaussian hypergeometric series as model problems, Prediction of unknown terms of a sequence and its application to some physical problems, Construction of new generalizations of Wynn's epsilon and rho algorithm by solving finite difference equations in the transformation order, Rational approximants using Levin-Weniger transforms, Rational interpolation using Levin-Weiniger transforms, Prediction proberties of Aitken's iterated \(\Delta^2\) process, of Wynn's epsilon algorithm, and of Brezinski's iterated theta algorithm

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the propagation of error in certain non-linear algorithms
• Error analysis of Aitken's \(\Delta^ 2\) process
• Toeplitz arrays, linear sequence transformations and orthogonal polynomials
• Accélération de la convergence en analyse numérique
• An Algorithm for a Generalization of the Richardson Extrapolation Process
• Automatic Selection of Sequence Transformations
• Numerical Comparisons of Nonlinear Convergence Accelerators
• The Set of Logarithmically Convergent Sequences Cannot be Accelerated
• On the Convergence and Stability of the Epsilon Algorithm
• Convergence Properties of Some Nonlinear Sequence Transformations
• Acceleration of Linear and Logarithmic Convergence
• Brève communication. Transformations de suites
• Development of non-linear transformations for improving convergence of sequences
• A Simple Method for Summing Certain Slowly Convergent Series
• On a Device for Computing the e m (S n ) Transformation