Treffer: On the power method in max algebra

Title:
On the power method in max algebra
Authors:
Elsner, Ludwig, van den Driessche, Pauline
Source:
Linear Algebra and its Applications. :17-32
Publisher Information:
Elsevier BV, 1999.
Publication Year:
1999
Subject Terms:
Numerical computation of eigenvalues and eigenvectors of matrices, spectral radius, Numerical Analysis, Algebra and Number Theory, power method algorithm, irreducible matrix, 16. Peace & justice, Inequalities involving eigenvalues and eigenvectors, nonnegative matrix, 01 natural sciences, Norms of matrices, numerical range, applications of functional analysis to matrix theory, eigenvalue problem, Discrete Mathematics and Combinatorics, Geometry and Topology, 0101 mathematics, norms, max algebra system
Document Type:
Fachzeitschrift Article<br />Conference object
File Description:
application/xml
Language:
English
ISSN:
0024-3795
DOI:
10.1016/s0024-3795(98)10171-4
Access URL:
https://zbmath.org/1419857
https://doi.org/10.1016/s0024-3795(98)10171-4
https://www.sciencedirect.com/science/article/abs/pii/S0024379598101714
http://www.yaroslavvb.com/papers/elsner-on.pdf
Rights:
Elsevier Non-Commercial
"In Copyright" Rights Statement
Accession Number:
edsair.doi.dedup.....1e728f63f76e6cff8de80e8ebd7ec4c3
Database:
OpenAIRE

Weitere Informationen

Let an eigenvalue problem \(A\otimes x=\lambda x\) be given with an irreducible and nonnegative matrix \(A\), \((A\otimes x)_i=\max_j(a_{ij}x_j)\) and \(\lambda\) turns out to be the maximum circuit geometric mean \(\mu(A)\). For computing \(\mu(A)\) and eigenvector \(x\) a power method algorithm is given and some asymptotic formulas relating \(\mu(A)\), the spectral radius and norms are also derived.