Error estimates for modified local Shepardʹs interpolation formula Original Research Article

The aim of this paper is to obtain error estimates for a modified local Shepardʹs approximation. This interpolation operator uses approximated Taylor polynomials at the data points glued together by a local Shepardʹs partition of unity. We introduce a condition number which is a geometric measure of the quality of the approximate derivatives obtained by least square fits of polynomials to function values at nearby nodes. The condition number is practically computable and it is closely related to the approximating power of the method. The error estimates obtained are important in the analysis of Galerkin approximations based on these Shepardʹs interpolation operators.