Study of a generalized Levin-Weniger convergence accelerator of numerical series: Particular cases and applications to multi-electron integrals in atomic physics

Authors:
Ignacio Porras;Francisco Cordobés-Aguilar
Affiliations:
Departamento de Física Atómica, Molecular y Nuclear, Facultad de Ciencias, Universidad de Granada, E-18071 Granada, Spain;Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
Venue:
Applied Numerical Mathematics
Year:
2010

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Abstract

In this work the general Levin transformation for a new remainder estimate is studied and compared to the u-transformation for some particular test cases. Also, the Weniger transformation and a generalization of both are studied specifically for the three-electron problem in atomic physics. In addition, we study the problem of the instability of these convergence accelerators and discuss attempts to reduce them.