Weniger, Ernst Joachim (2000) Prediction properties of Aitken's iterated Delta(2) process, of Wynn's epsilon algorithm, and of Brezinski's iterated theta algorithm. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 122 (1-2). pp. 329-356. ISSN 0377-0427
Full text not available from this repository.Abstract
The prediction properties of Aitken's iterated Delta(2) process, Wynn's epsilon algorithm, and Brezinski's iterated theta algorithm for (formal) power series are analyzed. As a first step, the defining recursive schemes of these transformations are suitably rearranged in order to permit the derivation of accuracy-through-order relationships. On the basis of these relationships, the rational approximants can be rewritten as a partial sum plus an appropriate transformation term. A Taylor expansion of such a transformation term, which is a rational function and which can be computed recursively, produces the predictions for those coefficients of the (formal) power series which were not used for the computation of the corresponding rational approximant. (C) 2000 Elsevier Science B.V. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GROUND-STATE ENERGY; ESTIMATING PERTURBATIVE COEFFICIENTS; NONLINEAR SEQUENCE TRANSFORMATIONS; PADE-APPROXIMANT PREDICTIONS; OCTIC ANHARMONIC-OSCILLATOR; FIXED-POINT SEQUENCES; QUANTUM-FIELD THEORY; CONVERGENCE ACCELERATORS; EXTRAPOLATION METHODS; FINITE CLUSTER; |
| Subjects: | 500 Science > 510 Mathematics 500 Science > 540 Chemistry & allied sciences |
| Divisions: | Chemistry and Pharmacy > Institut für Physikalische und Theoretische Chemie |
| Depositing User: | Petra Gürster |
| Date Deposited: | 05 May 2021 07:03 |
| Last Modified: | 05 May 2021 07:03 |
| URI: | https://pred.uni-regensburg.de/id/eprint/42180 |
Actions (login required)
 |
View Item |
