Robust Pade approximation via SVD


Trefethen, L


SIAM Review

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Pad e 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; a Matlab code is provided. The success of this
algorithm suggests that there might be variants of Pade approximation that would be pointwise
convergent as the degrees of the numerator and denominator increase to ∞, unlike traditional Pade approximants, which converge only in measure or capacity.

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Journal Article