Interpolation between sequence transformations
type: Item
instance of: scholarly article
title: Interpolation between sequence transformations
zbMATH Open document ID: 0794.65004
DOI: 10.1007/BF02141954
author: Ernst Joachim Weniger
published in: Numerical Algorithms
publication date: 1994-08-31T00:00:00Z
review text: It was found recently that Levin's transformation fails completely in convergence acceleration and summation processes, in the case of the strongly divergent Rayleigh-Schrödinger and renormalized perturbation expansions for the ground state energies of anharmonic oscillators, whereas the structurally very similar sequence transformation gives very good results. For a more detailed investigation of these phenomena, a sequence transformation is constructed which, depending on a continuous parameter, is able to interpolate between Levin's transformation and the other sequence transformation. Some numerical examples, which illustrate the properties of the interpolating sequence transformation, are presented.
Mathematics Subject Classification ID: 65B05
zbMATH DE Number: 440310
zbMATH Keywords: divergent series
zbMATH Keywords: Levin's transformation
zbMATH Keywords: convergence acceleration
zbMATH Keywords: summation
zbMATH Keywords: divergent Rayleigh-Schrödinger and renormalized perturbation expansions
zbMATH Keywords: ground state energies
zbMATH Keywords: anharmonic oscillators
zbMATH Keywords: sequence transformation
zbMATH Keywords: numerical examples
reviewed by: José L. Fernández Muñiz
describes a project that uses: HURRY
describes a project that uses: Maple
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02141954
OpenAlex ID: W2016823418
description: scientific article; zbMATH DE number 440310