  In this paper we investigate some practical aspects concerning the use of the
Restricted-Denominator (RD) rational Arnoldi method for the computation of the
core functions of exponential integrators for parabolic problems. We derive
some useful a-posteriori bounds together with some hints for a suitable
implementation inside the integrators. Numerical ex- periments arising from the
discretization of sectorial operators are pre- sented.

Numerical Analysis