The sign regularity of the auxiliary family gi( x) = xαi(−ln x) βi in convergence acceleration processes using the E-algorithm

The E-algorithm can be successfully applied to accelerate the convergence of the solution of some numerical differential equations provided the respective error expansion satisfies a certain asymptotic determinantal condition. In this work it is proved that such condition is fulfilled for any error...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 1996-03, Vol.67 (2), p.237-253
Main Author: GRACA, M. M
Format: Article
Language:English
Subjects:
Acceleration of convergence
Convergence acceleration
E-algorithm
Error expansion
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
Sign regularity
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Description
Summary:The E-algorithm can be successfully applied to accelerate the convergence of the solution of some numerical differential equations provided the respective error expansion satisfies a certain asymptotic determinantal condition. In this work it is proved that such condition is fulfilled for any error expansion in which formation enter the auxiliary family h n α i (−ln h n ) β i (where h n designates the stepsize of the discretization method).
ISSN:0377-0427
1879-1778
DOI:10.1016/0377-0427(95)00016-X