Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Joseph Haraldson，加拿大滑铁卢大学
Inviter:
Title:	Finding the Nearest Non-Trivial Smith Normal Form
Time & Venue:	2019.3.8 10:00 N421
Abstract:	We consider the problem of computing the nearest matrix polynomial with a non-trivial Smith Normal Form (SNF). This is a non-convex optimization problem where we find a nearby matrix polynomial with prescribed eigenvalues and associated multiplicity structure in the invariant factors. Some recent results are discussed that show that computing the SNF of a matrix polynomial is amenable to numeric computation as an optimization problem. Furthermore, effective optimization techniques to find a nearby matrix polynomial with a non-trivial SNF are discussed. The results are then generalized to include the computation of a matrix polynomial having a maximum specified number of ones in the SNF (i.e., with a maximum specified McCoy rank).