Bivariate Interpolation in Rectangular Form

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...

Bivariate mean value interpolation on circles of the same radius

We consider   bivariate  mean-value interpolationproblem, where the integrals over circles are interpolation data. In this case the problem  is described  over   circles of the same radius and with  centers are on astraight line and it is shown that in this case the interpolation is not correct.

Shepard's Method of "Metric Interpolation" to Bivariate and Multivariate Interpolation

Shepard developed a scheme for interpolation to arbitrarily spaced discrete bivariate data. This scheme provides an explicit global representation for an interpolant which satisfies a maximum principle and which reproduces constant functions. The interpolation method is basically an inverse distance formula which is generalized to any Euclidean metric. These techniques extend to include interpo...

Error bounds for bivariate piecewise hermite interpolation