Homeier, Herbert H. H. (1998) An asymptotically hierarchy-consistent, iterative sequence transformation for convergence acceleration of Fourier series. NUMERICAL ALGORITHMS, 18 (1). pp. 1-30. ISSN 1017-1398, 1572-9265
Full text not available from this repository.Abstract
We derive the I transformation, an iterative sequence transformation that is useful for the convergence acceleration of certain Fourier series. The derivation is based on the concept of hierarchical consistency in the asymptotic regime. We show that this sequence transformation is a special case of the J transformation; Thus, many properties of the I transformation can be deduced from the known properties of the J transformation (like the kernel, determinantal representations, and theorems on convergence behavior and stability). Besides explicit formulas for the kernel, some basic convergence theorems for the I transformation are given here. Further, numerical results are presented that show that suitable variants of the I transformation are powerful nonlinear convergence accelerators for Fourier series with coefficients of monotonic behavior.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | EXPANSIONS; ALGORITHM; SUMMATION; convergence acceleration; extrapolation; summation of divergent series; hierarchical consistency; algorithms |
| Subjects: | 500 Science > 540 Chemistry & allied sciences |
| Divisions: | Chemistry and Pharmacy > Institut für Physikalische und Theoretische Chemie |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 01 Mar 2023 09:41 |
| Last Modified: | 01 Mar 2023 09:41 |
| URI: | https://pred.uni-regensburg.de/id/eprint/50276 |
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