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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
  • Convergence Acceleration
  • ε-Algorithm
  • Padé Approximants
Disciplines
  • Computer Science
  • Mathematics

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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