MITACS Seminar Series on Mathematics of Computer Algebra and Analysis

Normal Forms of Polynomial Matrices

Howard Cheng, Department of Mathematics and Computer Science, University of Lethbridge

Wednesday June 4th, 2008 at 3:30pm in K9509.

Abstract: 

Normal forms for polynomial matrices are used in applications such as
control theory.  The Hermite form, row-reduced form, weak Popov form 
and Popov form are introduced.  It is shown how these normal forms can
be computed by straightforward elimination-based algorithms.  In many 
cases, elimination-based approaches are insufficient because of 
intermediate expression swell on the coefficients.  Fraction-free and 
modular algorithms for these problems are briefly outlined.