Jentschura, Ulrich D. and Mohr, Peter J. and Soff, Gerhard and Weniger, Ernst Joachim (1999) Convergence acceleration via combined nonlinear-condensation transformations. COMPUTER PHYSICS COMMUNICATIONS, 116 (1). pp. 28-54. ISSN 0010-4655,
Full text not available from this repository. (Request a copy)Abstract
A method of numerically evaluating slowly convergent monotone series is described. First, we apply a condensation transformation due to Van Wijngaarden to the original series. This transforms the original monotone series into an alternating series. In the second step, the convergence of the transformed series is accelerated with the help of suitable nonlinear sequence transformations that are known to be particularly powerful for alternating series. Some theoretical aspects of our approach are discussed. The efficiency, numerical stability, and wide applicability of the combined nonlinear-condensation transformation is illustrated by a number of examples. We discuss the evaluation of special functions close to or on the boundary of the circle of convergence, even in the vicinity of singularities. We also consider a series of products of spherical Bessel functions, which serves as a model for partial wave expansions occurring in quantum electrodynamic bound state calculations. (C) 1999 Elsevier Science B.V.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ORDER BINDING CORRECTIONS; GROUND-STATE ENERGY; OCTIC ANHARMONIC-OSCILLATOR; LEVIN-WENIGER TRANSFORMS; RIEMANN ZETA-FUNCTION; SEQUENCE TRANSFORMATIONS; LAMB SHIFT; ASYMPTOTIC REPRESENTATION; HYPERGEOMETRIC FUNCTION; PERTURBATION-SERIES; computational techniques; quantum electrodynamics (specific calculations); calculations and mathematical techniques in atomic and molecular physics; numerical approximation and analysis |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Chemistry and Pharmacy > Institut für Physikalische und Theoretische Chemie |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 29 Nov 2022 11:05 |
| Last Modified: | 29 Nov 2022 11:05 |
| URI: | https://pred.uni-regensburg.de/id/eprint/48631 |
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