Generalized barycentric coordinates and approximations of convex functions on arbitrary convex polytopes
نویسندگان
چکیده
منابع مشابه
Generalized barycentric coordinates and approximations of convex functions on arbitrary convex polytopes
In this paper, we study the error in the approximation of a convex function obtained via a one-parameter family of approximation schemes, which we refer to as barycentric approximation schemes. For a given finite set of pairwise distinct points Xn := {xi}ni=0 in R, the barycentric approximation of a convex function f is of the form:
متن کاملBarycentric coordinates for convex polytopes
An extension of the standard barycentric coordinate functions for simplices to arbitrary convex polytopes is described. The key to this extension is the construction, for a given convex polytope, of a unique polynomial associated with that polytope. This polynomial, the adjoint of the polytope, generalizes a previous two-dimensional construction described by Wachspress. The barycentric coordina...
متن کاملApproximations of differentiable convex functions on arbitrary convex polytopes
Let Xn := {xi}ni=0 be a given set of (n + 1) pairwise distinct points in R (called nodes or sample points), let P = conv(Xn), let f be a convex function with Lipschitz continuous gradient on P and λ := {λi}ni=0 be a set of barycentric coordinates with respect to the point set Xn. We analyze the error estimate between f and its barycentric approximation:
متن کاملOn the monotonicity of generalized barycentric coordinates on convex polygons
Article history: Received 6 August 2015 Received in revised form 28 January 2016 Accepted 29 January 2016 Available online 11 February 2016
متن کاملBarycentric coordinates for convex sets
In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous applications in various fields as it allows smooth interpolation of data located on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation in higher di...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2013
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2013.07.014