72 citations · 87 across the 5 of their papers we have counts for
7 papers
Tropical tensor product and beyond
Peter Butkovic, Miroslav Fiedler
Our aim is to introduce the tropical tensor product and investigate its properties. In particular we show its use for solving tropical matrix equations.
On Tropical Linear and Integer Programs
Peter Butkovic
We present simple compact proofs of the strong and weak duality theorems of tropical linear programming. It follows that there is no duality gap for a pair of tropical primal-dual…
On the max-algebraic core of a nonnegative matrix
Peter Butkovic, Hans Schneider, Sergei Sergeev
The max-algebraic core of a nonnegative matrix is the intersection of column spans of all max-algebraic matrix powers. Here we investigate the action of a matrix on its core. Being…
Two cores of a nonnegative matrix
Peter Butkovic, Hans Schneider, Sergei Sergeev +1
We prove that the sequence of eigencones (i.e., cones of nonnegative eigenvectors) of positive powers A^k of a nonnegative square matrix A is periodic both in max algebra and in no…
Z-matrix equations in max algebra, nonnegative linear algebra and other semirings
Peter Butkovic, Hans Schneider, Sergei Sergeev
We study the max-algebraic analogue of equations involving Z-matrices and M-matrices, with an outlook to a more general algebraic setting. We show that these equations can be solve…
On visualisation scaling, subeigenvectors and Kleene stars in max algebra
Sergei Sergeev, Hans Schneider, Peter Butkovic
The purpose of this paper is to investigate the interplay arising between max algebra, convexity and scaling problems. The latter, which have been studied in nonnegative matrix the…