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Interpolation between sequence transformations

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Abstract

Levin's sequence transformation [1] and a structurally very similar sequence transformation [4] behave quite differently in convergence acceleration and summation processes. In particular, it was found recently that Levin's transformation fails completely in the case of the strongly divergent Rayleigh-Schrödinger and renormalized perturbation expansions for the ground state energies of anharmonic oscillators, whereas the structurally very similar sequence transformation gives very good results [14,17]. For a more detailed investigation of these phenomena, a sequence transformation is constructed which — depending on a continuous parameter — is able to interpolate between Levin's transformation and the other sequence transformation. Some numerical examples, which illustrate the properties of the interpolating sequence transformation, are presented.

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  1. Institut für Physikalische und Theoretische Chemie, Universität Regensburg, D-8400, Regensburg, Germany

    Ernst Joachim Weniger

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  1. Ernst Joachim Weniger
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Weniger, E.J. Interpolation between sequence transformations. Numer Algor 3, 477–486 (1992). https://doi.org/10.1007/BF02141954

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