C1 surface interpolation with constraints

Givenn pairwise distinct and arbitrarily spaced pointsPi in a domainD of thex−y plane andn real numbersfi, consider the problem of computing a bivariate functionf(x, y) of classC1 inD whose values inPi are exactlyfi,i=1,…,n, and whose first or second order partial derivatives satisfy appropriate equality and inequality constraints on a given set ofp pointsQl inD.In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires the solution of a large scale quadratic programming (QP) problem.The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem: such a method is very efficient and well suited for parallel implementation on a multiprocessor system.