Construction of new generalizations of Wynn’s epsilon and rho algorithm by solving finite difference equations in the transformation order

We construct new sequence transformations based on Wynn’s epsilon and rho algorithms. The recursions of the new algorithms include the recursions of Wynn’s epsilon and rho algorithm and of Osada’s generalized rho algorithm as special cases. We demonstrate the performance of our algorithms numericall...

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Veröffentlicht in:Numerical algorithms Jg. 83; H. 2; S. 593 - 627
Hauptverfasser: Chang, Xiang-Ke, He, Yi, Hu, Xing-Biao, Sun, Jian-Qing, Weniger, Ernst Joachim
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.02.2020
Springer Nature B.V
Schlagworte:
Algebra
Algorithms
Approximation
Computer Science
Difference equations
Dynamical systems
Mathematical functions
Numeric Computing
Numerical Analysis
Original Paper
Recipes
Sequences
Theory of Computation
Convergence acceleration algorithm
Sequence transformation
Epsilon algorithm
Rho algorithm
ISSN:1017-1398, 1572-9265
Online-Zugang:Volltext
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Zusammenfassung:We construct new sequence transformations based on Wynn’s epsilon and rho algorithms. The recursions of the new algorithms include the recursions of Wynn’s epsilon and rho algorithm and of Osada’s generalized rho algorithm as special cases. We demonstrate the performance of our algorithms numerically by applying them to some linearly and logarithmically convergent sequences as well as some divergent series.
Bibliographie:ObjectType-Article-1
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-019-00695-w