of a system of linear inequalities
A point at which the minimax
is attained. The problem of finding a Chebyshev point reduces to the general problem of linear programming .
A more general notion is that of a Chebyshev point of a system of hyperplanes in a Banach space , i.e. a point for which
Chebyshev points are often chosen as "solutions" of incompatible linear systems of equations and inequalities.
|||S.I. [S.I. Zukhovitskii] Zukhovitsky, L.I. Avdeeva, "Linear and convex programming" , Saunders (1966)|
|||P.K. Belobrov, "The Chebyshev point of a system of translates of subspaces in a Banach space" Mat. Zametki , 8 : 4 (1970) pp. 29–40 (In Russian)|
|||I.I. Eremin, "Incompatible systems of linear inequalities" Dokl. Akad. Nauk SSSR , 138 : 6 (1961) pp. 1280–1283 (In Russian)|
The term "Chebyshev point" or "Chebyshev nodeChebyshev node" is also used to denote a zero of a Chebyshev polynomial (cf. Chebyshev polynomials) in the theory of (numerical) interpolation, integration, etc. [a1].
Sometimes Chebyshev is spelled differently as Tschebyshev or Tschebycheff.
|[a1]||L. Fox, I. Parker, "Chebyshev polynomials in numerical analysis" , Oxford Univ. Press (1968)|
Chebyshev point. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Chebyshev_point&oldid=14353