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