نتایج جستجو برای: g doubly stochastic matrix

تعداد نتایج: 913790  

Journal: :Experimental Mathematics 1999
Clara S. Chan David P. Robbins

We study the calculation of the volume of the polytope Bn of n × n doubly stochastic matrices; that is, the set of real non-negative matrices with all row and column sums equal to one. We describe two methods. The first involves a decomposition of the polytope into simplices. The second involves the enumeration of “magic squares”, i.e., n×n non-negative integer matrices whose rows and columns a...

Journal: :CoRR 2009
Yaming Yu

It is convenient to define H(X) = Hα(X) = −∞ when X is discrete, e.g., degenerate. (Our notation differs from that of Karlin and Rinott 1981 here.) We study the entropy of a weighted sum, S = ∑n i=1 aiXi, of i.i.d. random variables Xi, assuming that the density f of Xi is log-concave, i.e., supp(f) = {x : f(x) > 0} is an interval and log f is a concave function on supp(f). The main result is th...

Journal: :Automatica 2012
Behrouz Touri Angelia Nedic

We study the ergodicity of backward product of stochastic and doubly stochastic matrices by introducing the concept of absolute infinite flow property. We show that this property is necessary for ergodicity of any chain of stochastic matrices, by defining and exploring the properties of a rotational transformation for a stochastic chain. Then, we establish that the absolute infinite flow proper...

2009

In this paper we introduce an approximate optimization framework for solving graphs problems involving doubly stochastic matrices. This is achieved by using a low dimensional formulation of the matrices and the approximate solution is achieved by a simple subgradient method. We also describe one problem that can be solved using our method.

Journal: :Proceedings of the ... AAAI Conference on Artificial Intelligence 2023

Doubly stochastic matrix plays an essential role in several areas such as statistics and machine learning. In this paper we consider the optimal approximation of a square set doubly matrices. A structured BFGS method is proposed to solve dual primal problem. The resulting algorithm builds curvature information into diagonal components true Hessian, so that it takes only additional linear cost o...

2010
ALLAN SLY

We investigate the properties of uniform doubly stochastic random matrices, that is non-negative matrices conditioned to have their rows and columns sum to 1. The rescaled marginal distributions are shown to converge to exponential distributions and indeed even large sub-matrices of side-length o(n) behave like independent exponentials. We determine the limiting empirical distribution of the si...

Journal: :Proceedings of the American Mathematical Society 1967

Journal: :wavelet and linear algebra 2014
f. khalooei

for vectors x, y ∈ rn, it is said that x is left matrix majorizedby y if for some row stochastic matrix r; x = ry. the relationx ∼` y, is defined as follows: x ∼` y if and only if x is leftmatrix majorized by y and y is left matrix majorized by x. alinear operator t : rp → rn is said to be a linear preserver ofa given relation ≺ if x ≺ y on rp implies that t x ≺ ty onrn. the linear preservers o...

Journal: :Electr. J. Comb. 2009
Jessica Striker

The Birkhoff (permutation) polytope, Bn, consists of the n × n nonnegative doubly stochastic matrices, has dimension (n− 1)2, and has n2 facets. A new analogue, the alternating sign matrix polytope, ASMn, is introduced and characterized. Its vertices are the Qn−1 j=0 (3j+1)! (n+j)! n × n alternating sign matrices. It has dimension (n− 1)2, has 4[(n− 2)2 +1] facets, and has a simple inequality d...

Journal: :Discrete & Computational Geometry 2014
Nathan Linial Zur Luria

Let us denote by Ωn the Birkhoff polytope of n× n doubly stochastic matrices. As the Birkhoff–von Neumann theorem famously states, the vertex set of Ωn coincides with the set of all n× n permutation matrices. Here we consider a higherdimensional analog of this basic fact. Let Ω n be the polytope which consists of all tristochastic arrays of order n. These are n×n×n arrays with nonnegative entri...

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