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Construction of new generalizations of Wynn’s epsilon and rho algorithm by solving finite difference equations in the transformation order. (English) Zbl 1507.65005

Summary: 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.

MSC:

65B05 Extrapolation to the limit, deferred corrections
65B10 Numerical summation of series

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