Franz Peherstorfer, Klaus Schiefermayr,
"Description of extremal polynomials on several intervals and their computation II"
, in Acta Mathematica Hungarica, Vol. 83, Seite(n) 59-83, 1999
Description of extremal polynomials on several intervals and their computation II
Sprache des Titels:
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 E if l+1 boundary points of E and the number of extremal points in each interval of E 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.