Bivariate interpolation of potential functions

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...

Cubic pencils of lines and bivariate interpolation

Abstract: Cubic pencils of lines are classified up to projectivities. Explicit formulae for the addition of lines on the set of nonsingular lines of the pencils are given. These formulae can be used for constructing planar generalized principal lattices, which are sets of points giving rise to simple Lagrange formulae in bivariate interpolation. Special attention is paid to the irreducible nons...

Error bounds for bivariate piecewise hermite interpolation

Bivariate Lagrange Interpolation at the Chebyshev Nodes

We discuss Lagrange interpolation on two sets of nodes in two dimensions where the coordinates of the nodes are Chebyshev points having either the same or opposite parity. We use a formula of Xu for Lagrange polynomials to obtain a general interpolation theorem for bivariate polynomials at either set of Chebyshev nodes. An extra term must be added to the interpolation formula to handle all poly...