Discrete tchebycheff approximation for multivariate splines

Multivariate Splines for Data Fitting and Approximation

Methods for scattered data fitting using multivariate splines will be surveyed in this paper. Existence, uniqueness, and computational algorithms for these methods, as well as their approximation properties will be discussed. Some applications of multivariate splines for data fitting will be briefly explained. Some new research initiatives of scattered data fitting will be outlined. §

Quasiinterpolants and Approximation Power of Multivariate Splines

The determination of the approximation power of spaces of multivariate splines with the aid of quasiinterpolants is reviewed. In the process, a streamlined description of the existing quasiinterpolant theory is given. 1. Approximation power of splines I begin with a brief review of the approximation power of univariate splines since the techniques for its investigation are also those with which...

Multivariate Discrete Splines and Linear Diophantine Equations

In this paper we investigate the algebraic properties of multivariate discrete splines. It turns out that multivariate discrete splines are closely related to linear diophantine equations. In particular, we use a solvability condition for a system of linear diophantine equations to obtain a necessary and sufficient condition for the integer translates of a discrete box spline to be linearly ind...

Tchebycheff Approximation in a Compact Metric Space

B Ivariate Approximation by Discrete Smoothing Pde Splines

This paper deals with the construction and characterization of discrete PDE splines. For this purpose, we need a PDE equation (usually an elliptic PDE), certain boundary conditions and a set of points to approximate. We give two results about the convergence of a discrete PDE spline to a function of a fixed space in two different cases: (1) when the approximation points are fixed; (2) when the ...