The set-intersection function gives the cardinality of the intersection of two sets. In order to obtain a lower bound for the communication complexity of this function, the rank of the corresponding characteristic function-value matrices was calculated in 4] and 5]. In this note, the rank of these matrices is determined by another method of proof, which makes use of a factorization into a produ...

We study the freeness problem for matrix semigroups. We show that the freeness problem is decidable for upper-triangular 2×2 matrices with rational entries when the products are restricted to certain bounded languages. We also show that this problem becomes undecidable for large enough matrices. The full version of this work was accepted for publication in Information and Computation. It is ava...

It is shown that a real Hankel matrix admits an approximate block diagonalization in which the successive transformation matrices are upper triangular Toeplitz matrices. The structure of this factorization was first fully discussed in [1]. This approach is extended to obtain the quotients and the remainders appearing in the Euclidean algorithm applied to two polynomials u(x) and v(x) of degree ...

Iterative methods for solving sparse triangular systems are an attractive alternative to exact forward and backward substitution if an approximation of the solution is acceptable. On modern hardware, performance benefits are available as iterative methods allow for better parallelization. In this paper, we investigate how block-iterative triangular solves can benefit from using overlap. Because...

We determine the number of isomorphism classes elementary gradings by a finite group on an algebra upper block-triangular matrices. As consequence we prove that, for abelian G , sequence numbers E ( m ) -gradings M F × matrices with entries in field characterizes . A formula over algebraically closed field, mild restrictions its characteristic, is also provided. Finally, if group, and N that ∼ ...

Recently, Jeĺınek derived that the number of self-dual interval orders of reduced size n is twice the number of row-Fishburn matrices of size n by using generating functions. In this paper, we present a bijective proof of this relation by establishing a bijection between two variations of upper-triangular matrices of nonnegative integers. Using the bijection, we provide a combinatorial proof of...

We present an upper bound O(n 2) for the mixing time of a simple random walk on upper triangular matrices. We show that this bound is sharp up to a constant, and nd tight bounds on the eigenvalue gap. We conclude by applying our results to indicate that the asymmetric exclusion process on a circle indeed mixes more rapidly than the corresponding symmetric process.

A QR–method for computing the singular values via semiseparable matrices. Abstract The standard procedure to compute the singular value decomposition of a dense matrix, first reduces it into a bidiagonal one by means of orthogonal transformations. Once the bidiagonal matrix has been computed, the QR–method is applied to reduce the latter matrix into a diagonal one. In this paper we propose a ne...

This paper proposes a two-stage fuzzy logarithmic preference programming with multi-criteria decisionmaking, in order to derive the priorities of comparison matrices in the analytic hierarchy pprocess (AHP) and the analytic network process (ANP). The Fuzzy Preference Programming (FPP) proposed by Mikhailov and Singh [L. Mikhailov, M.G. Singh, Fuzzy assessment of priorities with application to c...