Fall 2001 GSS Schedule

Organizers: Jeff Farr

Date Speaker Topic Abstract
August 27 Jeff Farr A Slowly Convergent Sequence We consider a sequence, p_n, defined by
p_0=0,
p_1=1,
p_n= 1/2 * p_{n/3} + 1/2*p_{n/2}, n > 1.
This is a simple example of a sequence in which the nth term is a weighted average of the preceding terms and the weights for p_n are heavily concentrated at two previous elements in the sequence. It is known that if the weights for the nth therm of a sequence are sharply concentrated around a single previous element and if the sequence appears to be oscillating at the beginning, then the sequence will continue to oscillate, and, hence, will not converge. Although the double-biased sequence which we consider appears to be oscillating at the beginning, we show that it does, in fact, slowly converge. Specifically, we prove that p_n converges to 2/(1 + log_2(3)). This talk will focus on various estimation techniques that were needed to show that the sequence converges.
pdf file
September 3 Labor Day
September 10 Kelly Waters The Finite Element Method and the Glowinski-Pironneau Pressure Decomposition for the Modified Stokes Problem We present the Finite Element Method (FEM) applied to a simple one-dimentional problem:
u" = f,
u(0) = 0,
u'(1) = 0,
The intent is to give the audience a general idea of what FEM means. In much less detail we present our current application of the Glowinski-Pironneau pressure decomposition to the modified Stokes problem. pdf file
September 17 Art Gorka The Methods of Feasible Directions The Methods of Feasible Directions (MFD) are used for solving inequality constrained Nonlinear Programming problems