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

DOI:
https://doi.org/10.1090/S0025-5718-1982-0645665-1

MathSciNet review:
645665

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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 method, Wynn's algorithm, Brezinski's 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 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

DOI:
https://doi.org/10.1090/S0025-5718-1982-0645665-1

Keywords:
Acceleration of convergence,
iterated Aitken's ,
algorithm,
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