Symbolic Computation Group

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

Friday, Nov, 9, 2012 , at U. of Western Ontario
Basic Theory and Algorithm of Numerical Factorization of Polynomials
Wenyuan Wu, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences

Abstract: Conventional factorization is an ill-posed problem for general multivariate polynomials and univariate polynomials with multiple roots, in the sense that almost all perturbations alter the factorization structure completely so that numerical computation becomes intractable. In this talk we study the the geometry behind factorization and then formulate the notion of the numerical polynomial factorization as a generalization as well as approximation of the exact factorization based on its geometry, establish its existence, uniqueness, Lipschitz continuity, and convergence to the underlying exact factorization. We also proposes a basic algorithmic framework of the numerical factorization including the numerical square-free factorization and numerical reducibility test based on eigenvalue computation, numerical greatest common divisor, and Gauss-Newton iteration method.

 

Last modified on Thursday, 08 November 2012, at 18:33 hours.