Title :

On the kernel of vector ε-algorithm and related topics

Author(s) :

Brezinski, Claude [Auteur]
Université de Lille
Redivo-Zaglia, Michela [Auteur]
Università di studi di Padova - Dipartimento di studi linguistici e letterari [UP DISLL]
Salam, Ahmed [Auteur]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]

Journal title :

Numerical Algorithms
Numerical Methods and Scientific Computing CIRM, Luminy, France 8-12 November 2021

Pages :

207-221

Publisher :

Springer Verlag

Publication date :

2023-09

ISSN :

1017-1398

English keyword(s) :

vector ε-algorithm kernels Shanks transformation Aitken's ∆ 2 process Clifford algebra
vector ε-algorithm
kernels
Shanks transformation
Aitken's ∆ 2 process
Clifford algebra

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

The vector ε-algorithm of Wynn is a powerful method for accelerating the convergence of vector sequences. Its kernel is the set of sequences which are transformed into constant sequences whose terms are their limits or ...
Show more >The vector ε-algorithm of Wynn is a powerful method for accelerating the convergence of vector sequences. Its kernel is the set of sequences which are transformed into constant sequences whose terms are their limits or antilimits. In 1971, a sufficient condition characterizing sequences in this kernel was given by McLeod. In this paper, we prove that such a condition is not necessary. Moreover, using Clifford algebra, we give a formula for the vector ε 2-transformation, which is formally the same as in the scalar case, up to operations in a Clifford algebra. Hence, Aitken's ∆ 2 process is extended in this way to vectors. Then, we derive the explicit algebraic and geometric expressions of sequences of the kernel of the ε 2transformation. We also formulate a conjecture concerning the explicit algebraic expression of kernel of the vector ε-algorithm.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL