Unique Solvability in Bivariate Hermite Interpolation

Energy minimization method for scattered data Hermite interpolation

Given a set of scattered data with derivatives values, we use a minimal energy method to find Hermite interpolation based on bivariate spline spaces over a triangulation of the scattered data locations. We show that the minimal energy method produces a unique Hermite spline interpolation of the given scattered data with derivative values. Also we show that the Hermite spline interpolation conve...

Error bounds for bivariate piecewise hermite interpolation

Approximation order of bivariate spline interpolation for arbitrary smoothness

By using the algorithm of Nfimberger and Riessinger (1995), we construct Hermite interpolation sets for spaces of bivariate splines Sq(d 1 ) of arbitrary smoothness defined on the uniform type triangulations. It is shown that our Hermite interpolation method yields optimal approximation order for q >~ 3.5r + 1. In order to prove this, we use the concept of weak interpolation and arguments of Bi...

Piecewise Bivariate Hermite Interpolations for Large Sets of Scattered Data

The requirements for interpolation of scattered data are high accuracy and high efficiency. In this paper, a piecewise bivariate Hermite interpolant satisfying these requirements is proposed. We firstly construct a triangulation mesh using the given scattered point set. Based on this mesh, the computational point (x, y) is divided into two types: interior point and exterior point. The value of ...

Approximation by C Splines on Piecewise Conic Domains

We develop a Hermite interpolation scheme and prove error bounds forC bivariate piecewise polynomial spaces of Argyris type vanishing on the boundary of curved domains enclosed by piecewise conics.