Abstract
The aim of this paper is to use Eiermann's theorem to define precisely good poles for the Padé-type approximant of a certain class of functions. Stieltjes functions whose measure has a compact support or functions with a finite number of real singularities are the main examples of this study. The case of an approximant with one multiple pole is completely studied. The case of two poles is considered. Some numerical experiments have been done, showing that the results, obtained by majorization, seem optimal.
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References
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Van Iseghem, J. Best choice of the pole for the Padé-type approximant of a Stieltjes function. Numer Algor 3, 463–475 (1992). https://doi.org/10.1007/BF02141953
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DOI: https://doi.org/10.1007/BF02141953