Joseph
Haraldson,
PhD
candidate
David
R.
Cheriton
School
of
Computer
Science
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).