Electronic Resource
Springer
Constructive approximation
8 (1992), S. 309-329
ISSN:
1432-0940
Keywords:
30E10
;
41A50
;
33A65
;
Best approximation
;
Chebyshev polynomial
;
Optimal polynomial
;
Green's function
;
Disjoint intervals
;
Disjoint sets
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We are concerned with the problem of finding among all polynomials of degreen 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 alln. A closely related approximation problem is obtained by considering all polynomials that have degree no larger thann 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 alln.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01279022
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