Approximation Order from Certain Spaces of Smooth Bivariate Splines on a Three-Direction Mesh.

摘要

This paper studies the approximation order from certain spaces of smooth vibariate splines on a three-direction mesh. Approximation order is a measurement of how well an approximation scheme works. This concept is important in numerical analysis. Unlike the situation in univariate spline approximation, the task of determining approximation order of multivariate spline spaces is very difficult. This report opens up a way to attack this problem. It is hoped that this method may eventually lead to a complete solution of this problem.