A recursive algorithm for Hermite interpolation over a triangular grid
The authors propose a recursive algorithm to solve the bivariate Hermite interpolation polynomial problem for nodes arranged in a triangular grid, based on dynamic programming. This algorithm computes a single polynomial that interpolates the full set of data consisting of partial derivatives and mixed type partial derivatives up to some fixed order at the nodes of the grid. The interpolant is a polynomial with minimum degree bound when the order is identical for all nodes. The proposed algorithm is affinely invariant, has at least linear precision, is symmetric with respect to the grid directions and can reuse existing computations if points are added to the grid.
bivariate Hermite interpolation polynomial
scientific article; zbMATH DE number 947626
scientific article