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Distributions of Zeros and Poles of N-Point Padé Approximants to Complex-Symmetric Functions Defined at Complex Points

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Ukrainian Mathematical Journal Aims and scope

The knowledge of the location of zeros and poles of Padé and N-point Padé approximations to a given function f provides much valuable information about the investigated functions. In general, PAs reproduce the exact zeros and poles of the considered functions but, unfortunately, some spurious zeros and poles appear randomly. Then it is clear that the control of the position of poles and zeros becomes essential for the applications of the Padé-approximation method. The numerical examples included in the paper show how necessary for the convergence of PA is the knowledge of the positions of their zeros and poles. We perform our research of localization of the poles and zeros of PA and NPA for the case of Stieltjes functions because we are interested in the efficiency of numerical application of these approximations. These functions belong to the class of complex-symmetric functions. The PA and NPA to the Stieltjes functions in different regions of the complex plane are also analyzed. It is expected that the appropriate selection of the complex point for the definition of approximant may improve it as compared with the traditional choice of ζ = 0. All considered cases are graphically illustrated. Some unique numerical results presented in the paper are sufficiently regular and should motivate the reader to carefully think about them.

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Authors and Affiliations

  1. K. Pulaski University of Technology and Humanities, Radom, Poland

    R. Jedynak & J. Gilewicz

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  1. R. Jedynak
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  2. J. Gilewicz
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Correspondence to R. Jedynak.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 8, pp. 1034–1055, August, 2021. Ukrainian DOI: 10.37863/umzh.v73i8.333.

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Jedynak, R., Gilewicz, J. Distributions of Zeros and Poles of N-Point Padé Approximants to Complex-Symmetric Functions Defined at Complex Points. Ukr Math J 73, 1200–1224 (2022). https://doi.org/10.1007/s11253-022-01987-6

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  • DOI: https://doi.org/10.1007/s11253-022-01987-6

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