Accession Number:

ADA093575

Title:

Numerical Construction of Smooth Surfaces from Aggregated Data.

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

Report Date:

1980-10-01

Pagination or Media Count:

24.0

Abstract:

The numerical construction of a smooth surface with prescribed weighted integrals over a domain of interest, is investigated. This construction is mostly relevant to the estimation of a smooth density function over geographical regions, from data aggregated over several subregions. By analogy to the definition of the univariate histospline the smooth surface is defined as the solution to a certain constrained minimization problem. The application of finite element methods to the numerical solution of the minimization problem is studied. It is shown that any finite element procedure, convergent for a related boundary value problem can be used to construct a sequence of finite element approximations converging to the smooth surface which solves the constrained minimization problem. For the case of smoothness requirement of lowest order, a specific finite element method is considered, and its convergence as the mesh size decreases is demonstrated numerically for a particular example of volume matching. Author

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE