An algorithm for the generalized symmetric tridiagonal eigenvalue problem
type: Item
instance of: scholarly article
title: An algorithm for the generalized symmetric tridiagonal eigenvalue problem
zbMATH Open document ID: 0821.65018
DOI: 10.1007/BF02142694
author: Kuiyuan Li
author: Zhonggang Zeng
author: Tien-Yien Li
published in: Numerical Algorithms
publication date: 1995-09-27T00:00:00Z
review text: The authors propose an algorithm to solve numerically the generalized eigenvalue problem \(Tx = \lambda Sx\); \(T\), \(S\) being symmetric tridiagonal matrices. The algorithm is based on finding zeros of the polynomial equation \(\text{det} [T - \lambda S] = 0\); the characteristic polynomial and its derivatives can be evaluated by modified three-term recurrences. This equation is solved by Laguerre's iteration with starting point obtained by a split-merge process. Numerical results and discussion of advantages of the algorithm are also presented.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 720554
zbMATH Keywords: numerical results
zbMATH Keywords: algorithm
zbMATH Keywords: generalized eigenvalue problem
zbMATH Keywords: symmetric tridiagonal matrices
zbMATH Keywords: characteristic polynomial
zbMATH Keywords: three-term recurrences
zbMATH Keywords: Laguerre's iteration
reviewed by: Leonid Lebedev
describes a project that uses: LAPACK
describes a project that uses: CLAPACK
describes a project that uses: EISPACK
MaRDI profile type: Publication
cites work: Families of High Order Accurate Discretizations of Some Elliptic Problems
cites work: Q3259280
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: Q3359644
cites work: Symmetric matrix methods for Schrodinger eigenvectors
cites work: An Algorithm for the Banded Symmetric Generalized Matrix
cites work: An Algorithm for Symmetric Tridiagonal Eigenproblems: Divide and Conquer with Homotopy Continuation
cites work: A homotopy algorithm for a symmetric generalized eigenproblem
cites work: The Laguerre Iteration in Solving the Symmetric Tridiagonal Eigenproblem, Revisited
cites work: Q3868672
cites work: Parallel implementations for solving generalized eigenvalue problems with symmetric sparse matrices
cites work: Q3139297
cites work: Matrix eigensystem routines - EISPACK guide. 2nd ed
cites work: Q4127946
cites work: A scalable eigenvalue solver for symmetric tridiagonal matrices
cites work: Q5674306
description: scientific article; zbMATH DE number 720554