A Reduction Algorithm for Matrices Depending on a Parameter - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 1999

A Reduction Algorithm for Matrices Depending on a Parameter

Abstract

In this article, we study square matrices perturbed by a parameter $\epsilon$. An efficient algorithm computing the $\epsilon$-expansion of the eigenvalues in formal Laurent-Puiseux series is provided, for which the computation of the characteristic polynomial is not required. We show how to reduce the initial matrix so that the Lidskii-Edelman-Ma perturbation theory can be applied. We also explain why this approach may simplify the perturbed eigenvector problem. The implementation of the algorithm in the computer algebra system Maple has been used in a quantum mechanics context to diagonalize some perturbed matrices and is available.
Fichier principal
Vignette du fichier
JeaPfl1999.pdf (212.93 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03419442 , version 1 (08-11-2021)

Identifiers

  • HAL Id : hal-03419442 , version 1

Cite

Claude-Pierre Jeannerod, Eckhard Pflügel. A Reduction Algorithm for Matrices Depending on a Parameter. International Symposium on Symbolic and Algebraic Computation (ISSAC), Jul 1999, Vancouver, Canada. ⟨hal-03419442⟩

Collections

UGA CNRS LMC-IMAG
31 View
113 Download

Share

Gmail Facebook X LinkedIn More