A new technique of selection between sequence transformations
type: Item
instance of: scholarly article
title: A new technique of selection between sequence transformations
zbMATH Open document ID: 0889.65002
DOI: 10.1016/S0168-9274(97)00042-1
author: A. Fdil
published in: Applied Numerical Mathematics
publication date: 1998-06-18T00:00:00Z
review text: There are now many methods for acceleration of the convergence of sequences. However, given a slowly convergent sequence, it can be difficult to determine which convergence acceleration method will be effective. This paper describes a new method for automatically comparing results from different sequence acceleration methods and selecting the best method. The author proves exactness, acceleration, improvement and contraction theorems for the method. Many convergence acceleration methods provide a table of approximations to the sequence limit, where the columns or diagonals of such a table provide infinite families of sequence transformation methods. The author shows how the new selection method can be used for infinite families of methods. The paper concludes with a report about results from several numerical experiments. Example sequences with superlinear convergence, linear convergence, logarithmic convergence and alternating series convergence are used with nine different sequence transformation methods to illustrate the effectiveness of the new transformation selection method.
Mathematics Subject Classification ID: 65B05
zbMATH DE Number: 1072312
zbMATH Keywords: extrapolation
zbMATH Keywords: convergence acceleration
zbMATH Keywords: sequence transformation methods
zbMATH Keywords: selection method
zbMATH Keywords: numerical experiments
zbMATH Keywords: superlinear convergence
zbMATH Keywords: linear convergence
zbMATH Keywords: logarithmic convergence
zbMATH Keywords: alternating series convergence
reviewed by: A. Genz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1072312