We derive upper and lower bounds on the dimensions of trivariate spline spaces defined on tetrahedral partitions. The results hold for general partitions, and for all degrees of sm...
Learning function relations or understanding structures of data lying in manifolds embedded in huge dimensional Euclidean spaces is an important topic in learning theory. In this ...
In this paper we present a complete description of ideal projectors from the space of bivariate polynomials F[x; y] onto its subspace F<n[x; y] of polynomials of degree less tha...
This paper first provides a common framework for partial differential equation problems in both strong and weak form by rewriting them as generalized interpolation problems. Then ...
We consider the problem of constructing a C1 piecewise quadratic interpolant, Q, to positional and gradient data defined at the vertices of a tessellation of n-simplices in IRn . T...
In this paper we analyse a hybrid approximation of functions on the sphere S2 R3 by radial basis functions combined with polynomials, with the radial basis functions assumed to be...