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We present a novel method for calculating Pad\'e approximants that is capableof eliminating spurious poles placed at the point of development and ofidentifying and eliminating spurious poles created by precision limitationsand/or noisy coefficients. Information contained in in the eliminated poles isassimilated producing a reduced order Pad\'e approximant (PA). While the[m+k/m] conformation produced by the algorithm is flexible, the m value of therational approximant produced by the algorithm reported here is determined bythe number of spurious poles eliminated. Spurious poles due to coefficientnoise/precision limitations are identified using an evidence-based filterparameter applied to the singular values of a matrix comprised of the seriescoefficients. The rational function poles are found directly by solving ageneralized eigenvalue problem defined by a matrix pencil. Spurious poles placeat the point of development, responsible in some algorithms for degeneracy, areidentified by their magnitudes. Residues are found by solving an overdeterminedlinear matrix equation. The method is compared with the so-called Robust Pad\'eApproximation (RPA) method and shown to be competitive on the problems studied.By eliminating spurious poles, particularly in functions with branch points,such as those encountered solving the power-flow problem, solution of thesecomplex-valued problems is made more reliable.

The Pad\'e matrix pencil method with spurious pole information assimilation