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Computation of the c‐Table Related to the Padé Approximation

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  • Radosław Jedynak
  • Jacek Gilewicz

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.

Suggested Citation

  • Radosław Jedynak & Jacek Gilewicz, 2013. "Computation of the c‐Table Related to the Padé Approximation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:185648
    DOI: 10.1155/2013/185648
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    References listed on IDEAS

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    1. Radosław Jedynak & Jacek Gilewicz, 2013. "Approximation of the Integrals of the Gaussian Distribution of Asperity Heights in the Greenwood-Tripp Contact Model of Two Rough Surfaces Revisited," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, May.
    2. Radosław Jedynak & Jacek Gilewicz, 2013. "Approximation of the Integrals of the Gaussian Distribution of Asperity Heights in the Greenwood‐Tripp Contact Model of Two Rough Surfaces Revisited," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
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