DictionaryForumContacts

 drifting_along

link 27.02.2010 6:46 
Subject: flat corner (о симплекс-методе) math.
Не совсем понятно, что имеется в виду под flat corner.Если это угол, то почему тогда дальше идет фраза most corners of the polytope should have angles bounded away from being flat. Может, это вершина?
Вот контекст: Our analysis will exploit geometric properties of the condition number of a matrix, rather than of a linear program. We start with the observation that if a corner of a polytope is specified by the equation AIx = yI , where I is a d-set, then the condition number of the matrix AI provides a good measure of how far the corner is from being flat. Moreover, it is relatively easy to show that if A is subject to perturbation, then it is unlikely that AI has poor condition number. So, it seems intuitive that if A is perturbed, then most corners of the polytope should have angles bounded away from being flat. This already provides some intuition as to why the simplex method should run quickly: one should make reasonable progress as one rounds a corner if it is not too flat.

 

You need to be logged in to post in the forum

Get short URL | Photo