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Computation of the -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 -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.

Suggested Citation

  • Radosław Jedynak & Jacek Gilewicz, 2013. "Computation of the -Table Related to the Padé Approximation," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, November.
    • Handle: RePEc:hin:jnljam:185648
    DOI: 10.1155/2013/185648
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