Nonnegative Preserving Data Interpolation/Fitting based on Bivariate Splines

Applied and Computational Mathematics Seminar
Monday, April 7, 2014 - 14:00
1 hour (actually 50 minutes)
Skiles 005
University of Georgia
I mainly discuss the following problem: given a set of scattered locations and nonnegative values, how can one construct a smooth interpolatory or fitting surface of the given data?  This problem arises from the visualization of scattered data and the design of surfaces with shape control.  I shall start explaining scattered data interpolation/fitting based on bivariate spline functions over triangulation without nonnegativity constraint.  Then I will explain the difficulty of the problem of finding nonnegativity perserving interpolation and fitting surfaces and recast the problem into a minimization problem with the constraint. I shall use the  Uzawa algorithm to solve the constrained minimization problem. The convergence of the algorithm in the bivariate spline setting will be shown.  Several numerical examples will be demonstrated and finally a real life example for fitting oxygen anomalies over the Gulf of Mexico will be explained.