Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Numerical comparisons of nonlinear convergence accelerators

Authors: David A. Smith and William F. Ford
Journal: Math. Comp. 38 (1982), 481-499
MSC: Primary 65B10; Secondary 65-04
MathSciNet review: 645665
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65B10, 65-04

Retrieve articles in all journals with MSC: 65B10, 65-04

Additional Information

Keywords: Acceleration of convergence, iterated Aitken's $ {\Delta ^2}$, $ \varepsilon $ algorithm, $ \theta $ algorithm, Levin's transforms, linear convergence, logarithmic convergence, power series, Fourier series, power method, Bernoulli's method, asymptotic series, perturbation series, numerical tests
Article copyright: © Copyright 1982 American Mathematical Society