Speaker
Description
Over the last two decades, a number of methods for constructing linearizations of matrix polynomials have been developed, including ansatz spaces, Fiedler pencils, and block minimal basis pencils. These methods have also been extended in various ways to apply to matrix polynomials expressed in non-monomial bases. However, these extensions have often been achieved one basis at a time, without systematically investigating the possibility of useful relationships between linearizations for matrix polynomials expressed in different bases. This talk describes a unified framework for establishing strong connections between generalized ansatz spaces associated with different bases, enabling the immediate and explicit construction of large spaces of strong linearizations for matrix polynomials expressed in many of the classical polynomial bases.