Abstract
A method of optimizing a sequence of economized rational approximants (ERAs) to produce a sequence of approximants with enhanced convergence properties is described. It is shown that such a technique improves upon the error of the Padé approximants at a chosen value of the independent variable, and in some cases leads to dramatic improvement, even in cases where Padé approximants behave erratically. The procedure is tested on six known functions, with improved convergence and accuracy in each case. The procedure is then applied to the problem of evaluating a perturbation series of an atomic system, diamagnetic hydrogen, with significant improvement in both convergence and accuracy as well.
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