Approximation of Bivariate Functions via Smooth Extensions

Approximation of Bivariate Functions via Smooth Extensions

For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole ...

Quick approximation of bivariate functions.

This paper presents two experiments where participants had to approximate function values at various generalization points of a square, using given function values at a small set of data points. A representative set of standard function approximation models was trained to exactly fit the function values at data points, and models' responses at generalization points were compared to those of hum...

A sharp upper bound on the approximation order of smooth bivariate pp functions

A first result along these lines was given in [BH831] where it was shown that the approximation order of Π3,∆ (with ∆ the three-direction mesh) is only 3, which was surprising in view of the fact that all cubic polynomials are contained locally in this space. [J83] showed the corresponding result for C-quartics on the three-direction mesh and [BH832] provided upper and lower bounds for the appr...

A Sharp Upper Bound on the Approximation Order of Smooth Bivariate Pp Functions

Smooth Reenable Functions Provide Good Approximation Orders Smooth Reenable Functions Provide Good Approximation Orders

We apply the general theory of approximation orders of shift-invariant spaces of BDR1-3] to the special case when the nitely many generators L 2 (IR d) of the underlying space S satisfy an N-scale relation (i.e., they form a \father wavelet" set). We show that the approximation orders provided by such nitely generated shift-invariant spaces are bounded from below by the smoothness class of each...