Interpolation between sequence transformations. (English) Zbl 0794.65004
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.
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.
Reviewer: J.L.Fernández Muñiz (La Habana)
MSC:
| 65B05 | Extrapolation to the limit, deferred corrections |
Keywords:
divergent series; Levin’s transformation; convergence acceleration; summation; divergent Rayleigh-Schrödinger and renormalized perturbation expansions; ground state energies; anharmonic oscillators; sequence transformation; numerical examplesReferences:
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