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The present work deals with the rational model order reduction method basedon the single-point Least-Square (LS) Pad\'e approximation technique introducedin [3]. Algorithmical aspects concerning the construction of the rationalLS-Pad\'e approximant are described. In particular, the computation of thePad\'e denominator is reduced to the calculation of the eigenvectorcorresponding to the minimal eigenvalue of a Gramian matrix. The LS-Pad\'etechnique is employed to approximate the frequency response map associated tovarious parametric time-harmonic wave problems, namely, atransmission/reflection problem, a scattering problem and a problem inhigh-frequency regime. In all cases we establish the meromorphy of thefrequency response map. The Helmholtz equation with stochastic wavenumber isalso considered. In particular, for Lipschitz functionals of the solution, andtheir corresponding probability measures, we establish weak convergence of themeasure derived from the LS-Pad\'e approximant to the true one. 2D numericaltests are performed, which confirm the effectiveness of the approximationmethod.

Least-Squares Pad\'e approximation of parametric and stochastic Helmholtz maps