Notes on computing minimal approximant bases

2006/01/01 by Arne Storjohann, Storjohann, Arne · 3 citations
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Hermite Pade approximation #Numerical Methods and Algorithms #Polynomial and algebraic computation #minimal approximant bases

paper · doi:10.4230/dagsemproc.06271.12

openalex publication_date 2006/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (n₁,n₂,ldots,n_m), and order N := (n₁ + 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).

Cited by

• Using fast matrix multiplication to solve structured linear systems
• Fast, deterministic computation of the Hermite normal form and determinant of a polynomial matrix
• Faster Algorithms for Multivariate Interpolation with Multiplicities and Simultaneous Polynomial Approximations

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• Fast computation of approximant bases in canonical form
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