On a Quadratic Functional Occurring in a Bivariate Scattered Data Interpolation Problem

The application of widely known blending methods for constructing C1 bivariate functions interpolating scattered data requires the knowledge of the partial derivatives of first order at the vertices of an underlying triangulation. In this paper we consider the method proposed by Nielson that consists in computing estimates of the first order partial derivatives by minimizing an appropriate quadratic functional, characterized by nonnegative tension parameters. The aim of the paper is to analyse some peculiar properties of this func-tional in order to construct robust and efficient algorithms for determin-ing the above estimates of the derivatives when we are concerned with extremely large data sets