Interpolation between sequence transformations
It was found recently that Levin's transformation fails completely in convergence acceleration and summation processes, 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. 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.
divergent Rayleigh-Schrödinger and renormalized perturbation expansions
scientific article; zbMATH DE number 440310