From data-mining to nanotechnology and back: The new problems of numerical linear algebra

Monday, November 09, 2009

Presenter: Yousef Saad
Affiliation: University of Minnesota
Website: http://www.cs.umn.edu/~saad
Time: 11:15 - 12:15
Location: EE/CS 3-125 
Research in  numerical linear algebra  is changing rapidly  because of
the new  trends in the sciences  and the world  economy.  For example,
the current information revolution has given rise to a large number of
new challenges to computer scientists and mathematicians.  Many of the
numerical methods in scientific computing of the past few decades were
motivated  by  problems  originating  from  the  solution  of  Partial
Differential  Equations (PDEs)  -- as  a  response to  demands of  now
established   industries,  such  as   the  aerospace   and  automotive
industries.  A  few of  the new  trends that are  likely to  shape the
decades ahead  are: (1) Nanotechnology (e.g.   materials science), (2)
Biology  and genetics (3)  information technology.   In each  of these
applications there are enormously  challenging problems to solve which
require  matrix  algorithms that  are  far  more  powerful than  those
available  today.   I  will  discuss  a few  of  these  problems.   In
materials science,  the fundamental  equation is Schroedinger  and the
basic  problem is  an eigenvalue  problem with  many  eigenvalues.  In
information sciences,  one can mention  again clustering but  also the
broad problem  of dimensionality reduction  (e.g., Principal Component
Analysis) which is essential for handling huge data sets.

As the  title indicates,  this talk will  describe a journey  from the
problems  of  data mining,  to  those,  very  difficult, of  materials
science and then back toward the end, to discuss a new project whereby
data  mining is  exploited in  quantum modeling  too, in  a  new field
called ``materials informatics''.