Description of extremal polynomials on several intervals and their computation. II

F. Peherstorfer, K. Schiefermayr

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6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)59-83
Number of pages25
JournalActa Mathematica Hungarica
Volume83
Issue number1-2
Publication statusPublished - Apr 1999
Externally publishedYes

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