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Storjohann, Arne

Notes on computing minimal approximant bases

06271.StorjohannArne.Paper.776.pdf (0.1 MB)


We show how to transform the problem of computing solutions to a classical Hermite Pade approximation problem for an input vector of dimension $m imes 1$, arbitrary degree constraints $(n_1,n_2,ldots,n_m)$, and order $N := (n_1 + 1) + cdots + (n_m + 1) - 1$, to that of computing a minimal approximant basis for a matrix of dimension $O(m) imes O(m)$, uniform degree constraint $Theta(N/m)$, and order $Theta(N/m)$.

BibTeX - Entry

  author =	{Arne Storjohann},
  title =	{Notes on computing minimal approximant bases},
  booktitle =	{Challenges in Symbolic Computation Software},
  year =	{2006},
  editor =	{Wolfram Decker and Mike Dewar and Erich Kaltofen and Stephen Watt },
  number =	{06271},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Hermite Pade approximation, minimal approximant bases}

Keywords: Hermite Pade approximation, minimal approximant bases
Seminar: 06271 - Challenges in Symbolic Computation Software
Issue Date: 2006
Date of publication: 25.10.2006

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