## Numerical comparisons of nonlinear convergence accelerators

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- by David A. Smith and William F. Ford PDF
- Math. Comp.
**38**(1982), 481-499 Request permission

## Abstract:

As part of a continuing program of numerical tests of convergence accelerators, we have compared the iterated Aitken’s ${\Delta ^2}$ method, Wynn’s $\varepsilon$ algorithm, Brezinski’s $\theta$ algorithm, and Levin’s*u*transform on a broad range of test problems: linearly convergence alternating, monotone, and irregular-sign series, logarithmically convergent series, power method and Bernoulli method sequences, alternating and monotone asymptotic series, and some perturbation series arising in applications. In each category either the $\varepsilon$ algorithm or the

*u*transform gives the best results of the four methods tested. In some cases differences among methods are slight, and in others they are quite striking.

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## Additional Information

- © Copyright 1982 American Mathematical Society
- Journal: Math. Comp.
**38**(1982), 481-499 - MSC: Primary 65B10; Secondary 65-04
- DOI: https://doi.org/10.1090/S0025-5718-1982-0645665-1
- MathSciNet review: 645665