Computational and Applied Mathematics seminar

Abstract: The problem of approximating a given constant matrix $A$ by a matrix of prescribed rank $r<\min(m,n)$ is among the best understood problems in numerical linear algebra. The situation changes drastically if $A$ depends on parameters. In the talk we consider this problem for matrix polynomials, i.e., for $A(\lambda) \in \mathbb C[\lambda]^{m\times n}$. We present an algorithm for approximating $A(\lambda)$ by a matrix polynomial of prescribed rank and degree at most $d$. The method builds on recent advances in the theory of generic eigenstructures and factorizations of matrix polynomials with bounded rank and degree.