Chebyshev alternation
From Encyclopedia of Mathematics
A property of the difference between a continuous function 
on a closed set of real numbers 
and a polynomial 
(in a Chebyshev system 
) on an ordered sequence of 
points
 |
such that
 |
where 
or 
. The points 
are called Chebyshev alternation points or points in Chebyshev alternation (cf. also Alternation, points of).
Comments
Points in Chebyshev alternation are also called Chebyshev points of alternation, and their set is also called an alternating set. See also (the references in) Alternation, points of.
References
| [a1] | G.G. Lorentz, "Approximation of functions" , Holt, Rinehart & Winston (1966) pp. Chapt. 2, Sect. 6 |
How to Cite This Entry:
Chebyshev alternation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Chebyshev_alternation&oldid=13923
Chebyshev alternation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Chebyshev_alternation&oldid=13923
This article was adapted from an original article by Yu.N. Subbotin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article