Hyman's method revisited
type: Item
instance of: scholarly article
title: Hyman's method revisited
zbMATH Open document ID: 1181.65053
published in: Journal of Computational and Applied Mathematics
publication date: 2009-03-30T00:00:00Z
review text: The authors propose a method for multiple eigenvalues, which can be computed by the QR method in conjunction with the Newton method and Hyman's evaluation process using multiple precision. The authors derive a new general derivative formula for the characteristic polynomial and give the Jordan normal form of unreduced Hessenberg matrices in terms of the derivatives of the left and right eigenvectors. Finally, the authors demonstrate the applicability of the proposed method and numerical results are presented, using MATLAB.
reviewed by: George A. Gravvanis
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 5534928
zbMATH Keywords: QR method
zbMATH Keywords: multiple eigenvalues
zbMATH Keywords: Hessenberg matrices
zbMATH Keywords: Jacobian canonical form
zbMATH Keywords: Newton method
zbMATH Keywords: Hyman's method
author: Aurél Galántai
author: Csaba J. Hegedűs
describes a project that uses: mctoolbox
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: j.cam.2008.08.004
OpenAlex ID: W2095279657
cites work: Convergence of the shifted \(QR\) algorithm on \(3\times{} 3\) normal matrices
cites work: Q4435815
cites work: The effective order of singly-implicit Runge-Kutta methods
cites work: The construction of practical general linear methods
cites work: A multishift QR iteration without computation of the shifts
cites work: Perturbation bounds for polynomials
cites work: Hyman's Method Applied to the General Eigenvalue Problem
cites work: Remark on Algorithms to Find Roots of Polynomials
cites work: Q5185900
cites work: Q4864704
cites work: Q5543004
cites work: Matrix Analysis
cites work: Error analysis for the Newton-Raphson method
cites work: Determinantal expression and recursion for Jack polynomials
cites work: The Laguerre Iteration in Solving the Symmetric Tridiagonal Eigenproblem, Revisited
cites work: The Homotopy Continuation Algorithm for the Real Nonsymmetric Eigenproblem: Further Development and Implementation
cites work: Numerical methods for roots of polynomials. Part I
cites work: Hessenberg-triangular reduction and transfer function matrices of singular systems
cites work: Computation of transfer function matrices of linear multivariable systems
cites work: Sparse Hessenberg reduction and the eigenvalue problem for large sparse matrices
cites work: Laguerre's Method Applied to the Matrix Eigenvalue Problem
cites work: Canonical Decomposition of Hessenberg Matrices
cites work: Convergence of the Newton process to multiple solutions
cites work: Rational QR transformation with Newton shift for symmetric tridiagonal matrices
cites work: Q3677039
cites work: An approach to backward analysis for linear and nonlinear iterative methods
cites work: The behavior of a multiplicity independent root-finding scheme in the presence of error
cites work: Q4366793
cites work: Matrix algorithms. Vol. 2: Eigensystems
cites work: The QR Algorithm and Hyman's Method on Vector Computers
cites work: Q5674306
cites work: Q4871634
cites work: Numerical stability for solving nonlinear equations
cites work: Finding a Multiple Zero by Transformations and Newton-Like Methods
cites work: Hessenberg eigenvalue--eigenmatrix relations
DOI: 10.1016/J.CAM.2008.08.004
description: scientific article; zbMATH DE number 5534928