Introduction to the improved functional epsilon algorithm

[摘要] This paper introduces the improved functional epsilon algorithm. We have defined this new method in principle of the modified Aitken Delta(2) 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 Pade 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 Pade approximant is also demonstrated. Moreover, we illustrate the similarity between the integral Pade approximant and the modified Aitken Delta(2) algorithm; thus we have shown that the integral Pade approximant is a natural generalisation of modified Aitken Delta(2) algorithm. (C) 2002 Elsevier Science B.V. All rights reserved.

[发布日期] 2002-10-01

[关键词] improved functional epsilon algorithm;integral Pade approximant;convergence acceleration;modified Aitken Delta(2) algorithm;functional Pade approximant