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The epsilon algorithm an a non-commutative algebra

✍ Scribed by André Draux

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
522 KB
Volume
19
Category
Article
ISSN
0377-0427

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✦ Synopsis

In the case of a non-commutative algebra, the epsilon algorithm is deduced from the Pad6 approximants at t = 1, and from the use of the cross rule; their algebraic properties are a consequence of those verified by the Pad6 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 (AlSn) -l k-a --(ASn+i+i)i=j=o, for l =1, 2 and 3, have an inverse. Some results of convergence and convergence acceleration are also given.

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