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(2019.3.8)Joseph Haraldson:Finding the Nearest Non-Trivial Smith Normal Form
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Update time: 2019-03-04
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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

Joseph Haraldson

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).

 

 

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