A projection method for generalized eigenvalue problems using numerical integration.
type: Item
instance of: scholarly article
title: A projection method for generalized eigenvalue problems using numerical integration.
zbMATH Open document ID: 1037.65040
DOI: 10.1016/S0377-0427(03)00565-X
published in: Journal of Computational and Applied Mathematics
publication date: 2003-10-15T00:00:00Z
review text: The paper deals with the computational aspects of the generalized eigenvalue problem \(A=\lambda B\) where \(A\) and \(B\) are large \(n\times n\;\) matrices. The authors use the resolvent operator to construct a Weyl characteristic function whose poles are the eigenvalues. As expected, classical root finding methods fail when the eigenvalues are not real. To this end the authors compute contour integrals numerically and using the residue theorem to can detect and locate these eigenvalues. The error corresponding to the trapezoidal rule is analyzed and various examples can be found at the end of the paper.
reviewed by: Amin Boumenir
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 30E20
zbMATH DE Number: 1993206
zbMATH Keywords: generalized eigenvalue problem
zbMATH Keywords: spectral projection
zbMATH Keywords: large scale problem
zbMATH Keywords: numerical examples
zbMATH Keywords: resolvent operator
zbMATH Keywords: Weyl characteristic function
zbMATH Keywords: root finding methods
zbMATH Keywords: contour integrals
zbMATH Keywords: trapezoidal rule
author: Tetsuya Sakurai
author: Hiroshi Sugiura
describes a project that uses: JDQZ
MaRDI profile type: Publication
cites work: Q3138765
cites work: A generalized nonsymmetric Lanczos procedure
cites work: A Numerical Method for Locating the Zeros of an Analytic Function
cites work: Asymptotic waveform evaluation via a Lanczos method
cites work: A rational Lanczos algorithm for model reduction
cites work: Q3254327
cites work: Q3939931
cites work: Eigenvalue computation in the 20th century
cites work: Q5689624
cites work: Meso-scale fusion: A method for molecular electronic state calculation in inhomogeneous materials
cites work: Q4725623
cites work: An error analysis of two related quadrature methods for computing zeros of analytic functions.
cites work: On locating clusters of zeros of analytic functions
cites work: Computing the zeros of analytic functions
cites work: Computational Variants of the Lanczos Method for the Eigenproblem
cites work: A new look at the Lanczos algorithm for solving symmetric systems of linear equations
cites work: Rational Krylov sequence methods for eigenvalue computation
cites work: Using implicitly filtered RKS for generalised eigenvalue problems
cites work: A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
cites work: Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
description: scientific article; zbMATH DE number 1993206