\(C^ 1\) surface interpolation with constraints (Q1315241)

A method for solving the following problem is proposed: Given \(n\) pairwise distinct points \((x_ i,y_ i)\) in a domain \(D\) of \(\mathbb{R}^ 2\) and \(n\) real numbers \(f_ i\), one has to determine a function \(f\) in \(\mathbb{R}^ 2\) of class \(C^ 1(D)\) whose values in \((x_ i,y_ i)\) are \(f_ i\), and whose first or second order partial derivatives satisfy appropriate equality or inequality constraints on a given set of \(p\) points in \(D\). An iterative method for determining the solution of this problem is given.