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).
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