A simple application of the homotopy method to symmetric eigenvalue problems
type: Item
instance of: scholarly article
title: A simple application of the homotopy method to symmetric eigenvalue problems
zbMATH Open document ID: 0544.65019
DOI: 10.1016/0024-3795(84)90160-5
author: Moody T. Chu
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: If A is a symmetric tridiagonal matrix, the eigenvalue problem \(Ax=\lambda x\) is approached by a homotopy which connects A to a diagonal matrix D. It is shown that, under suitable conditions, there are exactly n solution curves connecting to the desired eigenvalues and eigenvectors. It is pointed out that sparse matrix techniques can be applied to the usual path following methods.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 3866466
zbMATH Keywords: homotopy method
zbMATH Keywords: symmetric tridiagonal matrix
zbMATH Keywords: sparse matrix techniques
zbMATH Keywords: path following methods
reviewed by: Georg Kreisel
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90160-5
OpenAlex ID: W2045349809
cites work: Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
cites work: Finding Zeroes of Maps: Homotopy Methods That are Constructive With Probability One
cites work: Q3862960
cites work: Nonlinear wave equations and constrained harmonic motion
cites work: On a numerical treatment for the curve-tracing of the homotopy method
cites work: Einige abstrakte Begriffe in der numerischen Mathematik (Anwendungen der Halbordnung).(Some abstract notions in the numerical mathematic. (Applications et semiorder))
cites work: A Theorem on Homotopy Paths
cites work: Q3928933
cites work: On Algorithms for Solvingf(x)=0
cites work: Q5510566
cites work: Nichtlineare Behandlung von Eigenwertaufgaben
description: scientific article; zbMATH DE number 3866466