Second Order Partial Derivatives Estimation Using a Modification of the Lagrange Quadratic Interpolant

Abstract

Partial derivative values are required to construct a smooth interpolated surface which passes through given three dimensional scattered data points. These partial derivative values are not avaliable in practice for raw three dimensional scattered data and the estimation of these values is thus desirable. This research concentrates on estimating the partial derivative values up to the second order. Many current methods concentrate on first order partial derivatives estimation as most applications require only up to the first order derivatives.