Chebyshev polynomials for disjoint compact sets

Bernd Fischer*

*Corresponding author for this work
15 Citations (Scopus)


We are concerned with the problem of finding among all polynomials of degree n with leading coefficient 1, the one which has minimal uniform norm on the union of two disjoint compact sets in the complex plane. Our main object here is to present a class of disjoint sets where the best approximation can be determined explicitly for all n. A closely related approximation problem is obtained by considering all polynomials that have degree no larger than n and satisfy an interpolatory constraint. Such problems arise in certain iterative matrix computations. Again, we discuss a class of disjoint compact sets where the optimal polynomial is explicitly known for all n.

Original languageEnglish
JournalConstructive Approximation
Issue number3
Pages (from-to)309-329
Number of pages21
Publication statusPublished - 01.09.1992


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