Computing Multivariate B-splines: A Simulation Based Approach

Nidhan Choudhuri

Statistics, CWRU

Refreshments: 3:30 - 4:00 p.m. Friday, Octbor 22, at 327 Yost
Talk: 4:00 - 5:00 p.m. Friday, October 22, at 327 Yost.

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 involved here. 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 are available today, based on a recurrence relation formula by Micchelli (1980). But the computing time there is too long and increases exponentially with thenumber 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. Some theoretical results will also be presented to support the validity of this procedure.

Questions? Nidhan Choudhuri