Introduction to the improved functional epsilon algorithm

Authors:
R. Thukral
Affiliations:
Padé Research Centre, 39 Deanswood Hill, West Yorkshire, Leeds LS17 5JS, England, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 5
Cited 1

Row convergence theorems for generalised inverse vector-valued Pade´ approximants

Journal of Computational and Applied Mathematics
A review of Pade´ methods for the acceleration of convergence of a sequence of vectors

Selected papers of the IMACS conference on Innovative methods in numerical analysis
Problems and progress in vector Pade´ approximation

Journal of Computational and Applied Mathematics - Special issue: ROLLS symposium
Row convergence theorems for vector-valued Padé approximants

Journal of Approximation Theory
A family of Padé-type approximants for accelerating the convergence of sequences

Journal of Computational and Applied Mathematics

Function-valued Padé-type approximant via the formal orthogonal polynomials and its applications in solving integral equations

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.30

Visualization

Abstract

This paper introduces the improved functional epsilon algorithm. We have defined this new method in principle of the modified Aitken Δ2 algorithm. Moreover, we have found that the improved functional epsilon algorithm has remarkable precision of the approximation of the exact solution and there exists a relationship with the integral Padé approximant. The use of the improved functional epsilon algorithm for accelerating the convergence of sequence of functions is demonstrated. The relationship of the improved functional epsilon algorithm with the integral Padé approximant is also demonstrated. Moreover, we illustrate the similarity between the integral Padé approximant and the modified Aitken Δ2 algorithm; thus we have shown that the integral Padé approximant is a natural generalisation of modified Aitken Δ2 algorithm.