  The present work deals with the rational model order reduction method based
on the single-point Least-Square (LS) Pad\'e approximation technique introduced
in [3]. Algorithmical aspects concerning the construction of the rational
LS-Pad\'e approximant are described. In particular, the computation of the
Pad\'e denominator is reduced to the calculation of the eigenvector
corresponding to the minimal eigenvalue of a Gramian matrix. The LS-Pad\'e
technique is employed to approximate the frequency response map associated to
various parametric time-harmonic wave problems, namely, a
transmission/reflection problem, a scattering problem and a problem in
high-frequency regime. In all cases we establish the meromorphy of the
frequency response map. The Helmholtz equation with stochastic wavenumber is
also considered. In particular, for Lipschitz functionals of the solution, and
their corresponding probability measures, we establish weak convergence of the
measure derived from the LS-Pad\'e approximant to the true one. 2D numerical
tests are performed, which confirm the effectiveness of the approximation
method.
