Homeier, Herbert H. H. (1999) Convergence acceleration of logarithmically convergent series avoiding summation. APPLIED MATHEMATICS LETTERS, 12 (3). pp. 29-32. ISSN 0893-9659,
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Quite often in application, logarithmically convergent series have to be evaluated. There are several convergence acceleration methods that are based on the evaluation of partial sums s(n) for relatively large n, and thus, normally require the evaluation of all terms a(j) with 0 less than or equal to j less than or equal to n. Here, we show that it is possible to avoid the computation of the partials sums of high order if it is possible to evaluate a few terms a(j) for relatively large j. The effectiveness of the approach is demonstrated for the 1/z expansion that is a particularly difficult example of logarithmic convergence. (C) 1999 Elsevier Science Ltd. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SEQUENCE TRANSFORMATIONS; EXTRAPOLATION; convergence acceleration; extrapolation; logarithmical convergence; E algorithm |
| Subjects: | 500 Science > 540 Chemistry & allied sciences |
| Divisions: | Chemistry and Pharmacy > Institut für Physikalische und Theoretische Chemie |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 19 Oct 2022 09:47 |
| Last Modified: | 19 Oct 2022 09:47 |
| URI: | https://pred.uni-regensburg.de/id/eprint/48254 |
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