In this paper, we consider the relationships between the second order linear recurrences, and the generalized doubly stochastic permanents and determinants. 1. Introduction The Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n 1 Fn+1 = Fn + Fn 1 (1.1) where F0 = 0; F1 = 1: The Lucas Sequence, fLng ; is de…ned by the recurrence relation, for n 1 Ln+1 = Ln + Ln 1 (1.2) where ...

We consider the convex polytope x(x) that consists of those n X n (row) stochastic matrices having a common nonnegative (left) fixed vector rt. We examine the l-skeleton of d(x) and show how to construct all extreme points adjacent to a given one (as vertices of the l-skeleton). Connections with transportation polytopes are discussed. Further, we give a formula for the degree of an extreme poin...

In Markov chain models in finance and healthcare a transition matrix over a certain time interval is needed but only a transition matrix over a longer time interval may be available. The problem arises of determining a stochastic pth root of a stochastic matrix (the given transition matrix). By exploiting the theory of functions of matrices, we develop results on the existence and characterizat...

Let Amx„, Bmxn, Xnxl, and Ymxl be matrices whose entries are nonnegative real numbers and suppose that no row of A and no column of B consists entirely of zeroes. Define the operators U, T and T by (UX)t-X? [or (UY),= Y;1], T=UB'UA and T' = UAUB'. Tis called irreducible if for no nonempty proper subset S of (1, • ■ ■ , n} it is true that X,=0, ieS; X,^0, i$ S, implies (TX),=0, ieS; (TX)i^O, i $...

In this paper, we propose Distributed Mirror Descent (DMD) algorithm for constrained convex optimization problems on a (strongly-)connected multi-agent network. We assume that each agent has a private objective function and a constraint set. The proposed DMD algorithm employs a locally designed Bregman distance function at each agent, and thus can be viewed as a generalization of the well-known...

Keywords: Google problem Power Method Stochastic matrices Global rate of convergence Gradient methods Strong convexity a b s t r a c t In this paper, we develop new methods for approximating dominant eigenvector of column-stochastic matrices. We analyze the Google matrix, and present an averaging scheme with linear rate of convergence in terms of 1-norm distance. For extending this convergence ...

For any stochastic matrix A of order n, denote its eigenvalues as λ1(A), . . . , λn(A), ordered so that 1 = |λ1(A)| ≥ |λ2(A)| ≥ . . . ≥ |λn(A)|. Let cT be a row vector of order n whose entries are nonnegative numbers that sum to n. Define S(c), to be the set of n × n row-stochastic matrices with column sum vector cT . In this paper the quantity λ(c) = max{|λ2(A)||A ∈ S(c)} is considered. The ve...

We present results regarding row and column spaces of matrices whose entries are elements of residuated lattices. In particular, we define the notions of a row and column space for matrices over residuated lattices, provide connections to concept lattices and other structures associated to such matrices, and show several properties of the row and column spaces, including properties that relate ...