HOMEIER, HHH (1995) DETERMINANTAL REPRESENTATIONS FOR THE J-TRANSFORMATION. NUMERISCHE MATHEMATIK, 71 (3). pp. 275-288. ISSN 0029-599X,
Full text not available from this repository.Abstract
The iterative J transformation [Homeier, H. H. H. (1993): Some applications of nonlinear convergence accelerators. Int. J. Quantum Chem. 45, 545-562] is of similar generality as the well-known E algorithm [Brezinski, C. (1980): A general extrapolation algorithm. Numer. Math. 35, 175-180. Havie, T. (1979): Generalized Neville type extrapolation schemes. BIT 19, 204-213]. The properties of the J transformation were studied recently in two companion papers [Homeier, H. H. H. (1994a): A hierarchically consistent, iterative sequence transformation. Numer. Algo; 8, 47-81. Homeier, H. H. H. (1994b): Analytical and numerical studies of the convergence behavior of the J transformation. J. Comput. Appl. Math., to appear]. In the present contribution, explicit determinantal representations for this sequence transformation are derived. The relation to the Brezinski-WaIz theory [Brezinski, C., Walt, G. (1991): Sequences of transformations and triangular recursion schemes, with applications in numerical analysis. J. Comput. Appl. Math. 34, 361-383] is discussed. Overholt's process [Overholt, K. J. (1965): Extended Aitken acceleration. BIT 5, 123-132] is shown to be a special case of the J transformation. Consequently, explicit determinantal representations of Overholt's process are derived which do not depend on lower order transforms. Also, families of sequences are given for which Overholt's process is exact. As a numerical example, the Euler series is summed using the J transformation. The results indicate that the J transformation is a very powerful numerical tool.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CONVERGENCE; SEQUENCES; |
| Depositing User: | Dr. Gernot Deinzer |
| Last Modified: | 19 Oct 2022 08:37 |
| URI: | https://pred.uni-regensburg.de/id/eprint/52367 |
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