Numerical comparisons of nonlinear convergence accelerators

As part of a continuing program of numerical tests of convergence accelerators, we have compared the iterated Aitken’s A2 method, Wynn’s e algorithm, Brezinski’s 0 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 e 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. © 1982 American Mathematical Society.

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Author David A. Smith Mathematics