On an accelerated procedure of extrapolation.
On Richardson Extrapolation for Finite Difference Methods on Regular Grids.
On the numerical computation of slowly convergent series.
Optimal Transformations for Scalar Sequences.
Optimalité du procédé d’Aitken pour l’accélération de la convergence linéaire
Power bounded prolongations and Picard-Lindelöf iteration.
Résultats négatifs en accélération de la convergence.
Sélection entre procédés d'accélération de la convergence
Sequence transformations and linear recurrences of higher order
Smoothing the Extrapolated Midpoint Rule
Some convergence acceleration processes for a class of vector sequences
Let be some vector sequence, converging to S, satisfying , where are constant vectors independent of n. The purpose of this paper is to provide acceleration methods for these vector sequences. Comparisons are made with some known algorithms. Numerical examples are also given.
Some fast finite-difference solvers for Dirichlet problems on general domains
The author proves the existence of the multi-parameter asymptotic error expansion to the five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on general domains. By Richardson extrapolation, this expansion leads to a simple process for accelerating the convergence of the method.
Some results on convergence acceleration for the E-algorithm
Some new results on convergence acceleration for the E-algorithm which is a general extrapolation method are obtained. A technique for avoiding numerical instability is proposed. Some applications are given. Theoretical results are illustrated by numerical experiments
Some results on nonlinear and nonlogarithmic sequences and their acceleration
Sur quelques limitations des algorithmes dans le traitement des suites
The combination of approximate solutions for accelerating the convergence
The General Neville-Aitken-Algorithm and Some Applications.
Two Composition Methods for Solving Certain Systems of Linear Equations.
Two step extrapolation and optimum choice of relaxation factor of the extrapolated S.O.R. method
Limits of the extrapolation coefficients are rational functions of several poles with the largest moduli of the resolvent operator and therefore good estimates of these poles could be calculated from these coefficients. The calculation is very easy for the case of two coefficients and its practical effect in finite dimensional space is considerable. The results are used for acceleration of S.O.R. method.
Une généralisation au cas vectoriel du procédé d’Aitken et les suites à comportement linéaire