Treffer: Fast and stable QR eigenvalue algorithms for generalized companion matrices and secular equations
Title:
Fast and stable QR eigenvalue algorithms for generalized companion matrices and secular equations
Authors:
Source:
Numerische Mathematik. 100:373-408
Publisher Information:
Springer Science and Business Media LLC, 2005.
Publication Year:
2005
Subject Terms:
Numerical computation of eigenvalues and eigenvectors of matrices, inverse power method, algorithm, eigenvalues, Inequalities involving derivatives and differential and integral operators, QR-factorization, 01 natural sciences, polynomial and rational equations, companion matrices, root-finder, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Computational aspects of field theory and polynomials, Numerical computation of solutions to single equations, 0101 mathematics
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
0945-3245
0029-599X
0029-599X
DOI:
10.1007/s00211-005-0595-4
Rights:
Springer TDM
Accession Number:
edsair.doi.dedup.....e20f57e7f768f8e8111b6e3285d30ef9
Database:
OpenAIRE
Weitere Informationen
The authors present a QR-based root-finder for some specific classes of polynomial and rational equations which runs in linear time per iteration and uses linear memory space. The algorithm computes the eigenvalues of some classes of \(n \times n\) generalized companion matrices by using \({\mathcal{O}}(n)\) arithmetic operations per iteration and with \({\mathcal{O}}(n)\) memory storage. As a main application, by using the already computed eigenvalues the whole set of eigenvectors can be computed efficiently by means of the inverse power method at the cost of \({\mathcal{O}}(n)\) flops per iteration.