Computing eigenvalues: Lanczos algorithm with a new recursive partitioning method
type: Item
instance of: scholarly article
title: Computing eigenvalues: Lanczos algorithm with a new recursive partitioning method
zbMATH Open document ID: 0942.65037
DOI: 10.1016/S0898-1221(99)00217-5
author: Yanyan Li
publication date: 2000-01-20T00:00:00Z
review text: In order to compute the eigenvalues of tridiagonal matrices obtained by applying the Lanczos algorithm to a symmetric matrix, the authors propose a recursion that combines the standard partitioning based on Sturm sequences with a local analysis that allows them to apply the Newton method when its convergence is ensured. The two numerical experiments reported suggest that a significant saving in computation time can be achieved.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1391656
zbMATH Keywords: Lanczos algorithm
zbMATH Keywords: bisection method
zbMATH Keywords: symmetric matrices
zbMATH Keywords: recursive partitioning algorithm
zbMATH Keywords: eigenvalues
zbMATH Keywords: tridiagonal matrices
zbMATH Keywords: Sturm sequences
zbMATH Keywords: Newton method
zbMATH Keywords: convergence
zbMATH Keywords: numerical experiments
reviewed by: Juan Pedro Milaszewicz
describes a project that uses: NAPACK
MaRDI profile type: Publication
cites work: Q5674306
cites work: Estimates for Some Computational Techniques in Linear Algebra
cites work: Eigenvalues of perturbed Hermitian matrices
cites work: The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
cites work: How to Implement the Spectral Transformation
cites work: The use of a refined error bound when updating eigenvalues of tridiagonals
cites work: A new look at the Lanczos algorithm for solving symmetric systems of linear equations
cites work: Q3321331
cites work: Q3994560
cites work: Q3407275
cites work: Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection
cites work: Solution of eigenvalue problems by sturm sequence method
full work available at URL: s0898-1221(99)00217-5
OpenAlex ID: W1980864648
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1391656