Computation of the c‐Table Related to the Padé Approximation

Radosław Jedynak and Jacek Gilewicz

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

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 c‐table analysis. We present an exhaustive list of useful formulas to compute a c‐table related to a formal power series C(z)=∑n=0∞cnzn. 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 c‐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 (c‐table) and in the version of Hankel determinants (c‐table). We compare the theory with numerical observations by reproducing different computational aspects of software producing the c‐tables with the presence of blocks and their evolution following the evolution of computer environment.

Date: 2013
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https://doi.org/10.1155/2013/185648

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:185648

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