We give simple necessary and sufficient conditions for the existence of a zero-one matrix with given row and column sums and at most one structural zero in each row and column. © 2006 Elsevier B.V. All rights reserved.

An alternating sign matrix [1] is a generalization of a permutation matrix. It consists of a matrix whose entries are 1, −1, and 0, and it satisfies the condition that in every row and column, the 1’s and −1’s alternate (possibly with 0’s in between) and the sum of the entries in every row or column is equal to 1 (so the permutation matrices are one type of these, in which there are no −1’s). F...

The present paper discusses the implementations of sparse matrix-vector products, which are crucial for high performance solutions of large-scale linear equations, on a PC-Cluster. Three storage formats for sparse matrices compressed row storage, block compressed row storage and sparse block compressed row storage are evaluated. Although using BCRS format reduces the execution time but the impr...

We consider designing a sparse sensing matrix which contains few non-zero entries per row for compressive sensing (CS) systems. By unifying the previous approaches for optimizing sensing matrices based on minimizing the mutual coherence, we propose a general framework for designing a sparse sensing matrix that minimizes the mutual coherence of the equivalent dictionary and is robust to sparse r...

The PageRank algorithm perturbs the adjacency matrix defined by a set of web pages and hyperlinks such that the resulting matrix is positive and row-stochastic. Applying the Perron-Frobenius theorem establishes that the eigenvector associated with the dominant eigenvalue exists and is unique. For some graphs, the PageRank algorithm may yield a canonical isomorph. We propose a ranking method bas...

In this paper a novel approach for matrix manipulation and indexing is proposed .Here the elements in a row of matrix are designated by numeric value called ‘permutation index’ followed by the elements of the row being randomised. This is done for all the rows of the matrix and in the end the set of permutation indices are put in the parent matrix and random locations depending on a pre decided...

In this paper we show how to construct diagonal scalings for arbitrary matrix pencils $\lambda B-A$, in which both $A$ and $B$ are complex matrices (square or nonsquare). The goal of such is “balance” some sense the row column norms pencil. We see that problem scaling a pencil equivalent sums particular nonnegative matrix. However, it known there exist square nonsquare cannot be scaled arbitrar...

This paper presents an approach for solving a nonlinear stochastic differential equations (NSDEs) using a new basis functions (NBFs). These functions and their operational matrices are used for representing matrix form of the NBFs. With using this method in combination with the collocation method, the NSDEs are reduced a stochastic nonlinear system of equations and unknowns. Then, the error ana...

This paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (TFs) in combination with the collocation method. The method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. Finally, the error analysis and some numerical examples are provided...

We consider a two player finite strategic zero-sum game where each player has stochastic linear constraints. We formulate the stochastic constraints of each player as chance constraints. We show the existence of a saddle point equilibrium if the row vectors of the random matrices, defining the stochastic constraints of each player, are elliptically symmetric distributed random vectors. We furth...