ISSN:
1572-9265
Keywords:
Sequence transformations
;
summation
;
divergent series
;
Rayleigh-Schrödinger and renormalized perturbation expansions
;
anharmonic oscillator
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02141954
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