Mathematics – Metric Geometry
Scientific paper
2008-07-07
Mathematics
Metric Geometry
26 pages, a minor revision
Scientific paper
This paper summarizes results on some topics in the max-plus convex geometry, mainly concerning the role of multiorder, Kleene stars and cyclic projectors, and relates them to some topics in max algebra. The multiorder principle leads to max-plus analogues of some statements in the finite-dimensional convex geometry and is related to the set covering conditions in max algebra. Kleene stars are fundamental for max algebra, as they accumulate the weights of optimal paths and describe the eigenspace of a matrix. On the other hand, the approach of tropical convexity decomposes a finitely generated semimodule into a number of convex regions, and these regions are column spans of uniquely defined Kleene stars. Another recent geometric result, that several semimodules with zero intersection can be separated from each other by max-plus halfspaces, leads to investigation of specific nonlinear operators called cyclic projectors. These nonlinear operators can be used to find a solution to homogeneous multi-sided systems of max-linear equations. The results are presented in the setting of max cones, i.e., semimodules over the max-times semiring.
No associations
LandOfFree
Multiorder, Kleene stars and cyclic projectors in the geometry of max cones does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Multiorder, Kleene stars and cyclic projectors in the geometry of max cones, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multiorder, Kleene stars and cyclic projectors in the geometry of max cones will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-560694