TY - JOUR
T1 - On the characterization of non-negative volume-matching surface splines
AU - Dyn, Nira
AU - Wong, Wing Hung
N1 - Funding Information:
* Done partially at the Mathematics Research Center, University of Wisconsin-Madison with the support of the U.S. Army under Contract No. DAAG29-75-C-0024. ’ Done partially at the Department of Statistics, University of Wisconsin-Madison support of the U.S. Army under Contract No. DAAG29-77-G-0207.
PY - 1987/9
Y1 - 1987/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=38249033680&partnerID=8YFLogxK
U2 - 10.1016/0021-9045(87)90089-X
DO - 10.1016/0021-9045(87)90089-X
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AN - SCOPUS:38249033680
VL - 51
SP - 1
EP - 10
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
SN - 0021-9045
IS - 1
ER -