Iteration schemes for the divide-and-conquer eigenvalue solver
type: Item
instance of: scholarly article
title: Iteration schemes for the divide-and-conquer eigenvalue solver
zbMATH Open document ID: 0809.65032
author: L. Gemignani
author: Dario A. Bini
published in: Numerische Mathematik
publication date: 1995-04-02T00:00:00Z
review text: The heart of the recent divide-and-conquer approaches is a method to update the eigenvalues of a matrix after a rank-1 update, which would in this case connect again parts of the matrix which had been deliberately broken in the divide stage. Here a globally convergent iteration scheme is proposed. The updating problem is split into the stages separation, isolation and approximation. The first stage separates the eigenvalues from the rest of the spectrum, the second stage isolates single eigenvalues, and the last stage approximates it up to the desired precision. The proposed method has the further advantage of having a lower sequential algorithmic complexity than other known methods. The results are demonstrated on some numerical examples.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 606964
zbMATH Keywords: iteration schemes
zbMATH Keywords: divide-and-conquer method
zbMATH Keywords: global convergence
zbMATH Keywords: eigenvalues
zbMATH Keywords: rank-1 update
zbMATH Keywords: algorithmic complexity
reviewed by: Hermann G. Matthies
MaRDI profile type: Publication
full work available at URL: s002110050035
OpenAlex ID: W2069044345
DOI: 10.1007/S002110050035
description: scientific article; zbMATH DE number 606964