Symbolic Computation Group

David R. Cheriton School of Computer Science
University of Waterloo, Waterloo, Ontario, Canada

Modular Factoring of Linear ODEs
Mark Giesbrecht, University of Waterloo
Friday, February 13, 2004, at U. of Western Ontario.

Abstract:

Factoring linear ODEs is an important step in their simplification and solution. As well as opening the door to (differential) Galois-theoretic methods, factoring can reduce a problem's size, making it more amenable to ad hoc techniques. While ``effective'' algorithms (i.e., algorithms which can be shown to terminate) for differential factoring have been known for a century, they are still extremely costly. On the other hand, for the related problem of factoring usual polynomials, great success has been achieved through modular methods: factor the polynomial modulo one or more primes and reconstruct a global factorization. In this talk I will discuss the problem of factoring linear ODEs via modular methods. I will present efficient algorithms for the first part of the problem, factoring ODEs and difference equations where the coefficients are from a function field over a finite field.

 

Last modified on Sunday, 04 November 2012, at 20:42 hours.