Abstract
In this paper we will consider a general mathematical concept of matching moments model reduction. The idea of model reduction via matching moments is well known and widely used in approximation of dynamical systems, but it goes back to Stieltjes, with some preceding work done by Chebyshev and Heine.
The algebraic moment matching problem can be formulated for a hermitian positive definite matrix as a variant of the Stieltjes moment problem and can be solved using Gauss-Christoffel quadrature. Using the operator moment problem suggested by Vorobyev, we will generalize model reduction based on matching moments to the non-Hermitian case in a straightforward way.
Unlike in the model reduction literature, the presented proofs follow directly from the construction of the Vorobyev moment problem.