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Notes on computing minimal approximant bases

Authors: Arne Storjohann

Published in: Dagstuhl Seminar Proceedings, Volume 6271, Challenges in Symbolic Computation Software (2006)

Abstract

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 $Theta(N/m)$.

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Arne Storjohann. Notes on computing minimal approximant bases. In Challenges in Symbolic Computation Software. Dagstuhl Seminar Proceedings, Volume 6271, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{storjohann:DagSemProc.06271.12,
  author =	{Storjohann, Arne},
  title =	{{Notes on computing minimal approximant bases}},
  booktitle =	{Challenges in Symbolic Computation Software},
  pages =	{1--6},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6271},
  editor =	{Wolfram Decker and Mike Dewar and Erich Kaltofen and Stephen Watt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06271.12},
  URN =		{urn:nbn:de:0030-drops-7763},
  doi =		{10.4230/DagSemProc.06271.12},
  annote =	{Keywords: Hermite Pade approximation, minimal approximant bases}
}

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Notes on computing minimal approximant bases

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