A simple rational interpolation method is given for estimating a frequency response matrix. The method is based on a generalization of the resolvent identity that avoids the potential inaccuracies introduced by the subtraction of nearly equal values in the calculation of the difference terms. When coupled with a pole cancellation method, the resulting interpolation algorithm is accurate and efficient. The error in this procedure has the form of a modified response matrix, which means that the interpolation algorithm can be used to approximate both the response matrix and the error.
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