论文信息 - Acceleration results for the vector E-algorithm

Acceleration results for the vector E-algorithm

AbstractIn this paper we are going to study the convergence and acceleration properties of the vector E-algorithm when applied to some families of vector sequences of the form $$S_n - S = \sum\limits_{i = 0}^k {or} {\text{ }}S_n - S \sim \sum\limits_{i = 0}^\infty {a_i g_i (n)}$$ withai∈ ℂ,gi(n) ∈ ℂp ∀i ⩾ 1. We will compare its properties with those of the scalar E-algorithm applied to each sequence of components and also the numerical stability of the two algorithms.

Ana C. Matos

[1] David A. Smith,et al. Acceleration of convergence of vector sequences , 1986 .

[2] Avram Sidi. Convergence and stability properties of minimal polynomial and reduced rank extrapolation algorithms , 1986 .

[3] C. Brezinski,et al. Accélération de la convergence en analyse numérique , 1977 .

[4] Avram Sidi,et al. Convergence and stability analyses for some vector extrapolation methods on the presence of defective iteration matrices , 1988 .

[5] Avram Sidi,et al. An algorithm for a generalization of the Richardson extrapolation process , 1987 .

[6] Claude Brezinski,et al. A general extrapolation algorithm , 1980 .

[7] J. Panovsky,et al. A family of implicit Chebyshev methods for the numerical integration of second- order differential equations , 1988 .

[8] S. Cabay,et al. A Polynomial Extrapolation Method for Finding Limits and Antilimits of Vector Sequences , 1976 .

[9] C. Brezinski. Generalisations de la transformation de shanks, de la table de Pade et de l'ε-algorithme , 1975 .

[10] M. Mesina. Convergence acceleration for the iterative solution of the equations X = AX + f , 1977 .

[11] A. U.S.. RECURSIVE ALGORITHMS FOR VECTOR EXTRAPOLATION METHODS , 2001 .

[12] Hassane Sadok. Accélération de la convergence de suites vectorielles et méthodes de point fixe , 1988 .

[13] R. P. Eddy. EXTRAPOLATING TO THE LIMIT OF A VECTOR SEQUENCE , 1979 .