Practical improvement of the divide-and-conquer eigenvalue algorithms
type: Item
instance of: scholarly article
title: Practical improvement of the divide-and-conquer eigenvalue algorithms
zbMATH Open document ID: 0756.65053
DOI: 10.1007/BF02241709
published in: Computing
publication date: 1992-09-27T00:00:00Z
review text: A practical modification of the well known divide-and-conquer algorithms for approximating the eigenvalues of a real symmetric tridiagonal matrix is presented. In this modification version the authors avoid the numerical stability problems of the algorithm but preserve the insensivity to clustering the eigenvalue and possibility to give upper bounds on the computational cost for any input matrix. Theoretical effectiveness of the algorithms is confirmed by numerical experiments.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 63398
zbMATH Keywords: divide-and-conquer algorithms
zbMATH Keywords: eigenvalues
zbMATH Keywords: symmetric tridiagonal matrix
zbMATH Keywords: numerical stability
zbMATH Keywords: clustering
zbMATH Keywords: computational cost
zbMATH Keywords: effectiveness
zbMATH Keywords: numerical experiments
author: Dario A. Bini
author: Victor Y. Pan
MaRDI profile type: Publication
cites work: Simple algorithms for approximating all roots of a polynomial with real roots
cites work: Iteration schemes for the divide-and-conquer eigenvalue solver
cites work: Q3138975
cites work: Rank-one modification of the symmetric eigenproblem
cites work: A Divide and Conquer method for the symmetric tridiagonal eigenproblem
cites work: A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem
cites work: An $O(N^2 )$ Method for Computing the Eigensystem of $N \times N$ Symmetric Tridiagonal Matrices by the Divide and Conquer Approach
cites work: Q3359644
cites work: Eigenvalues of a symmetric tridiagonal matrix: A divide-and-conquer approach
cites work: Q3868672
cites work: Eigenvalues of Symmetric Tridiagonal Matrices: A Fast, Accurate and Reliable Algorithm
cites work: Q3713483
cites work: On the worst-case arithmetic complexity of approximating zeros of polynomials
full work available at URL: https://doi.org/10.1007/bf02241709
OpenAlex ID: W135489932
description: scientific article; zbMATH DE number 63398