Haar space
From HandWiki
Revision as of 23:41, 9 May 2022 by imported>StanislovAI (correction)
In approximation theory, a Haar space or Chebyshev space is a finite-dimensional subspace [math]\displaystyle{ V }[/math] of [math]\displaystyle{ \mathcal C(X, \mathbb K) }[/math], where [math]\displaystyle{ X }[/math] is a compact space and [math]\displaystyle{ \mathbb K }[/math] either the real numbers or the complex numbers, such that for any given [math]\displaystyle{ f \in \mathcal C(X, \mathbb K) }[/math] there is exactly one element of [math]\displaystyle{ V }[/math] that approximates [math]\displaystyle{ f }[/math] "best", i.e. with minimum distance to [math]\displaystyle{ f }[/math] in supremum norm.[1]
References
- ↑ Shapiro, Harold (1971). Topics in Approximation Theory. Springer. pp. 19–22. ISBN 3-540-05376-X.
![]() | Original source: https://en.wikipedia.org/wiki/Haar space.
Read more |