127 research outputs found
Lower spectral radius and spectral mapping theorem for suprema preserving mappings
We study Lipschitz, positively homogeneous and finite suprema preserving
mappings defined on a max-cone of positive elements in a normed vector lattice.
We prove that the lower spectral radius of such a mapping is always a minimum
value of its approximate point spectrum. We apply this result to show that the
spectral mapping theorem holds for the approximate point spectrum of such a
mapping. By applying this spectral mapping theorem we obtain new inequalites
for the Bonsall cone spectral radius of max type kernel operators.Comment: arXiv admin note: text overlap with arXiv:1612.0175
Eigenproblems in addition-min algebra
In order to guarantee the downloading quality requirements of users and
improve the stability of data transmission in a BitTorrent-like peer-to-peer
file sharing system, this article deals with eigenproblems of addition-min
algebras. First, it provides a sufficient and necessary condition for a vector
being an eigenvector of a given matrix, and then presents an algorithm for
finding all eigenvalues and eigenvectors of a given matrix. It further proposes
a sufficient and necessary condition for a vector being a constrained
eigenvector of a given matrix and supplies an algorithm for computing all the
constrained eigenvectors and eigenvalues of a given matrix. This article
finally discusses the supereigenproblem of a given matrix and presents an
algorithm for obtaining the maximum constrained supereigenvalue and depicting
the feasible region of all the constrained supereigenvectors for a given
matrix. It also gives some examples for illustrating the algorithms,
respectively.Comment: 2
An Overview of Polynomially Computable Characteristics of Special Interval Matrices
It is well known that many problems in interval computation are intractable,
which restricts our attempts to solve large problems in reasonable time. This
does not mean, however, that all problems are computationally hard. Identifying
polynomially solvable classes thus belongs to important current trends. The
purpose of this paper is to review some of such classes. In particular, we
focus on several special interval matrices and investigate their convenient
properties. We consider tridiagonal matrices, {M,H,P,B}-matrices, inverse
M-matrices, inverse nonnegative matrices, nonnegative matrices, totally
positive matrices and some others. We focus in particular on computing the
range of the determinant, eigenvalues, singular values, and selected norms.
Whenever possible, we state also formulae for determining the inverse matrix
and the hull of the solution set of an interval system of linear equations. We
survey not only the known facts, but we present some new views as well
(K,L)-eigenvectors in max-min algebra
Using the concept of (K,L)-eigenvector, we investigate the structure of the
max-min eigenspace associated with a given eigenvalue of a matrix in the
max-min algebra (also known as fuzzy algebra). In our approach, the max-min
eigenspace is split into several regions according to the order relations
between the eigenvalue and the components of x. The resulting theory of
(K,L)-eigenvectors, being based on the fundamental results of Gondran and
Minoux, allows to describe the whole max-min eigenspace explicitly and in more
detail.Comment: New title and abstract, several minor correction
An iterative algorithm for computing the cycle mean of a Toeplitz matrix in special form
summary:The paper presents an iterative algorithm for computing the maximum cycle mean (or eigenvalue) of triangular Toeplitz matrix in max-plus algebra. The problem is solved by an iterative algorithm which is applied to special cycles. These cycles of triangular Toeplitz matrices are characterized by sub-partitions of
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