On the characterization of non-negative volume-matching surface splines

Nira Dyn, Wing Hung Wong

Research output: Contribution to journalArticlepeer-review


In this paper we study the surface spline which minimizes the Dirichlet Integral over a two-dimensional bounded domain, among all non-negative functions satisfying a finite number of volume-matching constraints. Existence and uniqueness of this surface spline are proved. A characterization by a variational inequality is given, revealing local and boundary behaviour of the surface spline. This characterization is of importance in the construction of numerical algorithms for the production of non-negative smooth surfaces from aggregated data.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalJournal of Approximation Theory
Issue number1
StatePublished - Sep 1987


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