ylfink@water.waterloo.edu (ylfink) (04/13/88)
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES
SYMBOLIC COMPUTATION SEMINAR
- Thursday, April 14, 1988
Dr. George Labahn, from the University of Alberta, will
speak on ``Matrix Pade Forms and Inverses of Block
Hankel Matrices''.
TIME: 3:30 PM
ROOM: MC 6082
ABSTRACT
Systems of equations where the coefficient matrix has
the structure of a block Hankel (or block Toeplitz)
matrix appear in many diverse branches of mathematics
and engineering. They are used, for example, in signal
processing and image processing (to calculate digital
filters), in algebraic computation (to calculate GCD's
of polynomials), and also in the determination of
rational approximants (matrix Pade forms) of a power
series.
In this talk we solve such systems by taking advantage
of the relationship between block Hankel matrices and
matrix Pade forms. An algorithm, MPADE, is given that
calculates matrix Pade forms of any type. This
algorithm also provides for an easy mechanism to decide
on the invertibility of the coefficient block Hankel
for our system. In the case where the matrix is indeed
invertible we present a set of closed inverse formulae
that are given in terms of the matrix Pade forms
calculated by MPADE. Thus we determine the inverse and
solve the system. This approach allows for significant
advantages in reliability, storage and efficiency over
existing methods. Directions for future research along
with interesting side-effects of our work will also be
presented.