We introduce a class of preconditioners for general sparsematrices based on the Birkhoff–von Neumann decomposition of doubly stochastic matrices. These preconditioners are aimed primarily at solving challenging linear systems with highly unstructured and indefinite coefficient matrices. We present some theoretical results and numerical experiments on linear systems from a variety of applications.

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.

The panstochastic analogue of Birkhoff's Theorem on doubly-stochastic matrices is proved in the case n = 5. It is shown that this analogue fails when n > 1, n = 5.

The panstochastic analogue of Birkhoff's Theorem on doubly-stochastic matrices is proved in the case n = 5. It is shown that this analogue fails when n > 1, n = 5.

We show that there exist bivariate proper quasi-copulas that do not induce a doubly stochastic signed measure on [0, 1]. We construct these quasi-copulas from the so-called proper quasitransformation square matrices.

The completely positive operators, which can be viewed as a generalization of the nonnegative matrices, are maps between spaces of linear operators arising in the study of C*-algebras. The existence of the operator analogues of doubly stochastic scalings of matrices is equivalent to a multitude of problems in computer science and mathematics, such rational identity testing in non-commuting vari...

Design matrices are sparse matrices in which the supports of different columns intersect in a few positions. Such matrices come up naturally when studying problems involving point sets with many collinear triples. In this work we consider design matrices with block (or matrix) entries. Our main result is a lower bound on the rank of such matrices, extending the bounds proven in [BDWY12, DSW14] ...

It is proved that a certain symmetric sequence (h0, h1, . . . , hd) of nonnegative integers arising in the enumeration of magic squares of given size n by row sums or, equivalently, in the generating function of the Ehrhart polynomial of the polytope of doubly stochastic n × n matrices, is equal to the h-vector of a simplicial polytope and hence that it satisfies the conditions of the g-theorem...