Solving Toeplitz- and Vandermonde-like linear systems with large displacement rank - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2007

Solving Toeplitz- and Vandermonde-like linear systems with large displacement rank

Abstract

Linear systems with structures such as Toeplitz-, Vandermonde-or Cauchy-likeness can be solved in $O\,\tilde{~}(\alpha^2 n)$ operations, where $n$ is the matrix size, $\alpha$ is its displacement rank, and $O\,\tilde{~}$ denotes the omission of logarithmic factors. We show that for Toeplitz-like and Vandermonde-like matrices, this cost can be reduced to $O\,\tilde{~}(\alpha^{\omega-1} n)$, where $\omega$ is a feasible exponent for matrix multiplication over the base field. The best known estimate for $\omega$ is $\omega < 2.38$, resulting in costs of order $O\,\tilde{~}(\alpha^{1.38} n)$. We also present consequences for Hermite--Pad\'e approximation and bivariate interpolation.
Fichier principal
Vignette du fichier
BoJeSc07.pdf (212.88 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03420744 , version 1 (09-11-2021)

Identifiers

Cite

Alin Bostan, Claude-Pierre Jeannerod, Éric Schost. Solving Toeplitz- and Vandermonde-like linear systems with large displacement rank. International Symposium on Symbolic and Algebraic Computation (ISSAC), Jul 2007, Waterloo, Canada. pp.33, ⟨10.1145/1277548.1277554⟩. ⟨hal-03420744⟩
29 View
137 Download

Altmetric

Share

Gmail Facebook X LinkedIn More