The epsilon algorithm and related topics

The epsilon algorithm is recommended as the best all-purpose acceleration method for slowly converging sequences. It exploits the numerical precision of the data to extrapolate the sequence to its limit. We explain its connections with Padé approximation and continued fractions which underpin its th...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 122; no. 1; pp. 51 - 80
Main Authors: Graves-Morris, P.R., Roberts, D.E., Salam, A.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.10.2000
Subjects:
Compass identity
Cross rule
Designant
Epsilon algorithm
Padé
qd algorithm
Star identity
Vector-valued approximant
Wynn
Star identity
Padé
Designant
Epsilon algorithm
Cross rule
Wynn
qd algorithm
Compass identity
Vector-valued approximant
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:The epsilon algorithm is recommended as the best all-purpose acceleration method for slowly converging sequences. It exploits the numerical precision of the data to extrapolate the sequence to its limit. We explain its connections with Padé approximation and continued fractions which underpin its theoretical base. Then we review the most recent extensions of these principles to treat application of the epsilon algorithm to vector-valued sequences, and some related topics. In this paper, we consider the class of methods based on using generalised inverses of vectors, and the formulation specifically includes the complex case wherever possible.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(00)00355-1