Maximum-entropy representations in convex polytopes: applications to spatial interaction
AbstractOf all representations of a given point situated in a convex polytope, as a convex combination of extreme points, there exists one for which the probability or weighting distribution has maximum entropy. The determination of this multiplicative or exponential distribution can be accomplished by inverting a certain bijection -- developed by Rothaus and by Bregman -- of convex polytopes into themselves. An iterative algorithm is available for this procedure. The doubly stochastic matrix with a given set of transversals (generalized diagonal products) can be found by means of this method. Applications are discussed of the Rothaus - Bregman map to a proof of Birkhoff's theorem and to the calculation of trajectories of points leading to stationary or equilibrium values of the generalized permanent, in particular in spatial interaction modeling.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Pion Ltd, London in its journal Environment and Planning A.
Volume (Year): 21 (1989)
Issue (Month): 11 (November)
Contact details of provider:
Web page: http://www.pion.co.uk
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Slater, Paul B., 1992. "Minimum relative entropies of low-dimensional spin systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(1), pages 145-154.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Neil Hammond).
If references are entirely missing, you can add them using this form.