# The epsilon algorithm an a non-commutative algebra

- Authors
- Journal
- Journal of Computational and Applied Mathematics 0377-0427
- Publisher
- Elsevier
- Publication Date
- Volume
- 19
- Issue
- 1
- Identifiers
- DOI: 10.1016/s0377-0427(87)80004-3
- Keywords
- Disciplines

## Abstract

Abstract In the case of a non-commutative algebra, the epsilon algorithm is deduced from the Padé approximants at t = 1, and from the use of the cross rule; their algebraic properties are a consequence of those verified by the Padé approximants. The computation of the coefficients is particularly studied. It is shown, that it does not exist any non-invertible needed elements if and only if the Hankel matrices M k (Δ′ S n ) = (Δ′ S n+i+j ) i=j=0 k−1 for l =1, 2 and 3, have an inverse. Some results of convergence and convergence acceleration are also given.

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