March 13: Nidhan Choudhuri

UNIVERSITY OF MINNESOTA

SEMINAR

School of Statistics
College of Liberal Arts

Computing Multivariate B-splines: A Simulation Based Approach

Nidhan Choudhuri
Department of Statistics
Case Western Reserve University

Monday, March 13, 2000
4:00-5:00 PM, Room B-15 Ford Hall
Social at 3:30 PM in Room 300 Ford Hall

Abstract

Univariate B-spline played an important role, both as a theoretical and practical tool, in dealing with polynomial splines; while its multivariate counterpart, despite of having all the theoretical properties of the univariate case, lacks application because of the computational difficulties. Unlike the univariate case, where there is an explicit form of the B-spline function, the multivariate B-spline is only implicitly defined and needs numerical approximation. Some computational procedures, based on a recurrence relation formula by Micchelli (1980), are available today. But the computing time there is too long and increases exponentially with the number of knots.

In this talk, we shall introduce a new simulation based procedure of computing a multivariate B-spline function, which is less time consuming and easy to implement. Theoretical results will also be presented to support the validity of this procedure.