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Description of Extremal Polynomials on Several Intervals and their Computation. II

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Abstract

First, T-polynomials, which were investigated in Part I, are used for a complete description of minimal polynomials on two intervals, of Zolotarev polynomials, and of polynomials minimal under certain constraints as Schur polynomials or Richardson polynomials. Then, based on an approach of W. J. Kammerer, it is shown that there exists a T-polynomial on a set of l intervals El if l + 1 boundary points of El and the number of extremal points in each interval of El are given. Finally, a fast algorithm for the numerical computation is provided and for two intervals it is demonstrated how to get T-polynomials with the help of Gröbner bases.

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Authors and Affiliations

  1. J. Kepler Universität Linz, A-4040, Linz, Austria

    F. Peherstorfer

  2. Institut für Algebra, Stochastik und Wissensbasierte Mathematische Systeme, J. Kepler Universität Linz, A-4040, Linz, Austria

    K. Schiefermayr

Authors
  1. K. Schiefermayr
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  2. F. Peherstorfer
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Schiefermayr, K., Peherstorfer, F. Description of Extremal Polynomials on Several Intervals and their Computation. II. Acta Mathematica Hungarica 83, 59–83 (1999). https://doi.org/10.1023/A:1006659402649

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