Functions of rational Krylov space matrices and their decay properties

Rational Krylov subspaces have become a fundamental ingredient in numerical linear algebra methods associated with reduction strategies. Nonetheless, many structural properties of the reduced matrices these are not fully understood. We advance this analysis by deriving bounds on entries rational and their functions, that ensure an a-priori decay as we move away from main diagonal. As opposed to other pattern results literature, hold spite lack any banded structure considered matrices. Numerical experiments illustrate quality our results.