cfry@watdcsu.waterloo.edu (C.Fry - Inst. Computer Research) (03/17/88)
Wavefront Eliminations
Renormalization
Fractals
by
Prof. Wei Pai Tang
of
Department of Computer Science
University of Waterloo
Abstract
During the 80's, the important driving forces in designing an op-
timal algorithm for large scale scientific computations are
hierarchical computation and parallelism. It is, in particular,
interesting to see that similar ideas have been also seen in phy-
sics - renormalization theory - and in mathematics - fractals -
in almost the same period. The new knowledge of a basic princi-
ple, namely the hierarchical self-similar structure of our mother
nature, has greatly enriched our repertoire of thought patterns.
In this talk, a new class of optimal fast solver - wavefront el-
imination - is studied using template operators. The results of
this study answer an open question: can a direct approach for
the model problem achieve optimal complexity? The basic idea
behind this algorithm can be interpreted as a renormalization
process and as recursively detailing a fractal. These interest-
ing connections have motivated us to apply the Wavefront Elimina-
tions to more general problems. The preliminary study shows that
this new direction is promising.
DATE: Wednesday, March 23, 1988
TIME: 3:30 p.m.
PLACE: MC 5158
Everyone is welcome. Refreshments served.