Case study in bivariate Hermite interpolation

Unique Solvability in Bivariate Hermite Interpolation

We consider the question of unique solvability in the context of bivariate Hermite interpolation. Starting from arbitrary nodes, we prescribe arbitrary conditions of Hermite type, and find an appropriate interpolation space in which the problem has a unique solution. We show that the coefficient matrix of the associated linear system is a nonsingular submatrix of a generalized Kronecker product...

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...

Hermite Birkhoff interpolation of scattered data by combined Shepard operators

Methods approaching the problem of the Hermite Birkhoff interpolation of scattered data by combining Shepard operators with local interpolating polynomials are not new in literature [1–4]. In [3] combinations of Shepard operators with bivariate Hermite-Birkhoff local interpolating polynomials are introduced to increase the algebraic degree of precision (polynomial reproduction degree) of Shepar...

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 ...