# 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

# Descriptors:

- *FINITE ELEMENT ANALYSIS
- *APPROXIMATION(MATHEMATICS)
- *FITTING FUNCTIONS(MATHEMATICS)
- NUMERICAL ANALYSIS
- MESH
- WEIGHTING FUNCTIONS
- ELLIPSOIDS
- BOUNDARY VALUE PROBLEMS
- DATA REDUCTION
- NUMERICAL METHODS AND PROCEDURES
- BIVARIATE ANALYSIS
- ITERATIONS
- SPLINES(GEOMETRY)
- THEOREMS
- LAPLACE TRANSFORMATION
- CURVE FITTING

# Subject Categories:

- Statistics and Probability