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

• Published in: Journal of computational and applied mathematics Vol. 67; no. 2; pp. 237 - 253
• Main Author: GRACA, M. M
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.1996; Elsevier
• 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; Sign regularity; Error expansion; E-algorithm; Convergence acceleration; Algorithms; Error analysis; Discretization; Numerical solution; Numerical methods; Differential equations; Discretization method
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/0377-0427(95)00016-X

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).