Case study in bivariate Hermite interpolation

Case study in bivariate Hermite interpolation

In this article we investigate the minimal dimension of a subspace of C1(R2) needed to interpolate an arbitrary function and some of its prescribed partial derivatives at two arbitrary points. The subspace in question may depend on the derivatives, but not on the location of the points. Several results of this type are known for Lagrange interpolation. As far as I know, this is the first such s...

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

Constrained Interpolation via Cubic Hermite Splines

Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation.  It is assumed here that the data is sufficiently accurate to warrant interpolation, rather than least ...

Bivariate hermite subdivision

A subdivision scheme for constructing smooth surfaces interpolating scattered data in 1~3 is proposed. It is also possible to impose derivative constraints in these points. In the case of functional data, i,e., data are given in a properly triangulated set of points {(x~, y~)}~=~ from which none of the pairs (xi, Yi) and (x j, gj) with i ~ j coincide, it is proved that the resulting surface (fu...