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Robust Padé approximation via SVD

By Pedro Gonnet, Stefan Guettel and Lloyd N. Trefethen


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

Topics: Approximations and expansions, Numerical analysis
Publisher: SIAM review
Year: 2011
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