CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM
                  UNIVERSITY OF COLORADO AT DENVER


TITLE:   Orthogonal Spline Collocation Matrix Decomposition Methods 
         for Elliptic Boundary Value Problems

SPEAKER: Graeme Fairweather, Mathematical and Computer Sciences,
         Colorado School of Mines

DATE:    Wednesday, May 3, 1995

PLACE:   Math Conference Room - Suite 540
         UCD Building, 1250 14th St., Denver

TIME:    2:30 pm (Refreshments served at 2:15 pm)

ABSTRACT: 
Fast direct methods are presented for the solution of the linear systems
arising in orthogonal spline collocation (OSC) -- spline collocation at Gauss
points -- applied to certain elliptic boundary value problems on rectangles.
 The methods, which are based on a matrix decomposition approach, involve the
solution of a generalized eigenvalue problem corresponding to the
discretization of a two-point boundary value problem.  The solution of the
original system is then reduced to solving a collection of independent almost
block diagonal linear systems which arise in OSC applied to one-dimensional
boundary value problems.  In this talk, we examine this approach applied to
second order separable linear problems (a) when bicubic Hermite approximating
functions are used, in which case the required eigensystem is known explicitly,
and (b) in the more general case of piecewise polynomials of arbitrary order.
The use of these techniques in algorithms for solving the biharmonic equation
is also described.