### Thursday, July 16

## MS51

Symbolic-Numeric Algorithms for Polynomials (Part I of II)

*This minisymposium is sponsored by Canadian Applied and Industrial Mathematics Society/Société Canadienne de Mathématiques Appliquées et Industrielles*
10:30 AM-12:30 PM

*Room: Sidney Smith 1073*

This minisymposium is intended to present a timely update to the emerging understanding of problems involving multivariate polynomials with inexactly- known coefficients. Such polynomial problems arise, for example, when physical measurements or numerical computations are used to specify a polynomial system. In particular, applications to computer-aided design are important already, and one expects a very wide array of applications to become important in the future.

One of the goals of holding this minisymposium is to stimulate interest in the numerical analysis community. While there is widespread activity in the computer algebra community, with an upcoming volume of the Journal of Symbolic Computation devoted to the topic, there are as yet only a handful of numerical analysts involved. Since the discovery that some important multivariate polynomial problems can and should be phrased instead as eigenvalue problems for nearly-commuting families of very large sparse matrices, it has become clear that there is a significant role for numerical analysis to play.

See Part II, MS66.

**Organizers: Robert M. Corless and Stephen M. Watt**

*University of Western Ontario, Canada*
**10:30 When Are Two Numeric Polynomials Relatively Prime?**
- George Labahn, University of Waterloo, Canada
**11:00 Multivariable Elimination Using Dixon Resultants**
*Deepak Kapur*, State University of New York, Albany; and Tushar Saxena, General Electric Corporate Research and Development
**11:30 On the Factorization of Approximate Multivariate Polynomials**
- Andre Galligo, Université de Nice, France; and
*Stephen M. Watt*, Organizer
**12:00 Solving Algebraic Systems Using Multi-Polynomial Resultants: Algorithms, Implementations, and Applications**
- Dinesh Manocha and
*Shankar Krishnan*, University of North Carolina, Chapel Hill

MMD Created: 3/19/98 Updated: 6/19/98