Frobenius-Padé́ is the name given to the class of rational approximants which, in the sense of Frobenius definition, generalizes the Padé approximation to the orthogonal series. New relations of recurrence are deduced involving the coefficients of the numerator, denominator and error series of four consecutive approximants belonging to two adjacent descendant diagonals of the Frobenius-Padé́ Table. Two algorithms for the recursive evaluation of Frobenius-Padé approximants are implemented in Fortran90 and Mathematica languages. The Fortran90 programmes were adapted in order to use the CADNA library to evaluate the cumulative effects of the computational errors and to consider only the digits that are correct in the results. We study the numerical stability and the conditioning computational issues of these approximants in an empiric sense, that is, the conclusions are based on the numerical results of a significant number of examples of different types.
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