主 题: Numerical Irreducible Factorization of Multivariate Polynomials
报告人: 吴文渊 （电子科技大学）
时 间: 2011-04-28 15:00-16:00
地 点: 理科一号楼1493
Computing the factorization by using floating point arithmetic of a polynomial is
an ill-posed problem since an arbitrarily small data perturbation could destroy the
reducibility and lead the polynomial to be irreducible. Consequently, it first requires a
proper regularization to a well-posed problem. This talk shows the geometry of the
factorization manifolds and establishes such a theory for Hadamard well-posedness.
Furthermore, based on Ruppert matrix and approximate Greatest Common Divisor
(GCD), a new method is given to compute numerical irreducible factorization (NIF)
of multivariate polynomials. Finally, the Gauss-Newton iteration refines the result
which is the exact factorization of a neaby problem with the desired factorization structure.