Robust Padé Approximation via SVD

Abstract

Padé approximation is considered from the point of view of robust methods of numerical linear algebra, in particular, the singular value decomposition. This leads to an algorithm for practical computation that bypasses most problems of solution of nearly-singular systems and spurious pole-zero pairs caused by rounding errors, for which a MATLAB code is provided. The success of this algorithm suggests that there might be variants of Padé approximation that are pointwise convergent as the degrees of the numerator and denominator increase to $\infty$, unlike traditional Padé approximants, which converge only in measure or capacity.