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.

Keywords

  1. Padé approximation
  2. SVD
  3. regularization
  4. Froissart doublet
  5. Nuttall--Pommerenke theorem

MSC codes

  1. 41A21
  2. 65F22

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Published In

cover image SIAM Review
SIAM Review
Pages: 101 - 117
ISSN (online): 1095-7200

History

Submitted: 28 October 2011
Accepted: 2 April 2012
Published online: 7 February 2013

Keywords

  1. Padé approximation
  2. SVD
  3. regularization
  4. Froissart doublet
  5. Nuttall--Pommerenke theorem

MSC codes

  1. 41A21
  2. 65F22

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