1. A Newton-type algorithm for solving an extremal constrained interpolation problem. Author Vlachkova, Krassimira Subjects *ALGORITHMS, *INTERPOLATION, *ITERATIVE methods (Mathematics), *NUMERICAL analysis, *LINEAR algebra, *ALGEBRA Abstract Given convex scattered data in R3 we consider the constrained interpolation problem of finding a smooth, minimal Lp-norm (1 < p < ∞) interpolation network that is convex along the edges of an associated triangulation. In previous work the problem has been reduced to the solution of a nonlinear system of equations. In this paper we formulate and analyse a Newton-type algorithm for solving the corresponding type of systems. The correctness of the application of the proposed method is proved and its superlinear (in some cases quadratic) convergence is shown. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR] Published 2000 Full Text View/download PDF