Bivariate Hermite Interpolation and Numerical Curves

Abstract

AbstractIn this paper, Hermite interpolation by bivariate algebraic polynomials of total degree ⩽nis considered. The interpolation parameters are the values of a function and its partial derivatives up to some ordernν−1 at the nodeszν=(xν, yν),ν=1, …, s, wherenνis the multiplicity ofzν. The sequence N={n1, …, ns; n} of multiplicities associated with the degree of interpolating polynomials is investigated. Some results of the paper were announced in [GHS93]