Numerical solution of the eigenvalue problem for efficiently structured Hermitian matrices
type: Item
instance of: scholarly article
title: Numerical solution of the eigenvalue problem for efficiently structured Hermitian matrices
zbMATH Open document ID: 0733.65020
DOI: 10.1016/0024-3795(91)90387-C
author: William F. Trench
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: For efficiently structured Hermitian matrices, which includes Hermitian Toeplitz plus Hankel matrices, the author introduces an \(O(n^ 2)\) FLOPS algorithm for finding specific eigenvalues, which draws onto the well- known Levinson algorithm for recursively solving equations for such matrices. The algorithm essentially uses the properties of Sturm sequences, and will work as long as the required eigenvalue is not too close to the spectrum of one of the principal minors. The paper includes numerical examples and tests to show the performance of the algorithm.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 4213319
zbMATH Keywords: efficiently structured Hermitian matrices
zbMATH Keywords: Hermitian Toeplitz plus Hankel matrices
zbMATH Keywords: FLOPS algorithm
zbMATH Keywords: eigenvalues
zbMATH Keywords: Levinson algorithm
zbMATH Keywords: Sturm sequences
zbMATH Keywords: numerical examples
zbMATH Keywords: performance
MaRDI profile type: Publication
cites work: Eigenvalues and eigenvectors of symmetric centrosymmetric matrices
cites work: Computing the Minimum Eigenvalue of a Symmetric Positive Definite Toeplitz Matrix
cites work: The “Pegasus” method for computing the root of an equation
cites work: Q3716207
cites work: Fast inversion algorithms of Toeplitz-plus-Hankel matrices
cites work: Toeplitz eigensystem solver
cites work: Q4195836
cites work: An Algorithm for the Inversion of Finite Hankel Matrices
cites work: Numerical Solution of the Eigenvalue Problem for Symmetric Rationally Generated Toeplitz matrices
cites work: Q5674306
description: scientific article; zbMATH DE number 4213319