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Journal of Applied Mathematics
Volume 2013, Article ID 185648, 10 pages
http://dx.doi.org/10.1155/2013/185648
Research Article

Computation of the -Table Related to the Padé Approximation

1Uniwersytet Technologiczno-Humanistyczny im. K. Pułaskiego, ul. Malczewskiego 20a, 26-600 Radom, Poland
2Aix Marseille Université, CPT CNRS, UMR 7332, Luminy, Case 907, 13288 Marseille Cedex 9, France
3Université de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France

Received 27 June 2013; Revised 13 September 2013; Accepted 24 September 2013

Academic Editor: Nicola Mastronardi

Copyright © 2013 Radosław Jedynak and Jacek Gilewicz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is to give a complete and practical method for numerical application of Padé approximation with the help of the -table analysis. We present an exhaustive list of useful formulas to compute a -table related to a formal power series . Some of these formulas are not widely known, because they were presented in publications of limited circulation. Some others were never published, as three symmetric Paszkowski-like formulas to overcome the blocks in a -table or an extension of local error formula for Padé approximants in the blocks. All formulas are given in two versions: in terms of Toeplitz determinants ( -table) and in the version of Hankel determinants ( -table). We compare the theory with numerical observations by reproducing different computational aspects of software producing the -tables with the presence of blocks and their evolution following the evolution of computer environment.