An alternate approach to solve two-level hierarchical time minimization transportation problem

This paper discusses a two-level hierarchical time minimization transportation problem, which is an important class of transportation problems arising in industries. This problem has been studied by various researchers (Sharma et al. in Eur J Oper Res 246:700–707, 2015; Sonia and Puri in TOP 12(2):301–330, 2004; Xie et al. in Comput Oper Res 86:124–139, 2017) and therefore, a number of polynomial time iterative algorithms are available to find its solution. All the existing algorithms, though efficient, have some shortcomings. The current study proposes an alternate solution algorithm for the problem that is more efficient in terms of computational time than the existing algorithms. The results justifying the underlying theory of the proposed algorithm are given. Further, a detailed comparison of the computational behaviour of all the algorithms for randomly generated instances of this problem, of different sizes validates the efficiency of the proposed algorithm.

     

Diameter preserving surjection on alternate matrices

Let F be a field with ｜F｜ ≥ 3, Km be the set of all m × m （m ≥ 4） alternate matrices over F. The arithmetic distance of A, B ∈ Km is d（A, B） ：= rank（A - B）. If d（A, B） = 2, then A and B are said to be adjacent. The diameter of Km is max{d（A, B） ： A, B ∈ km}. Assume that φ ： Km→Km is a map. We prove the following are equivalent： （a） φ is a diameter preserving surjection in both directions, （b） φ is both an adjacency preserving surjection and a diameter preserving map, （c） φ is a bijective map which preserves the arithmetic distance.     

Complex D convergence and diagonal convergence of matrices

In this paper, types of convergence (also referred to as Schur stability) for complex matrices are studied. In particular, it is proven that for complex matrices of order $n?3$ diagonal convergence, $D_{\mathbb{C}}$ convergence and boundary convergence are all equivalent. An example of a 4 by 4 matrix that is $D_{\mathbb{C}}$ convergent but not diagonally convergent is constructed.     

An alternate approach to axiomatizations of the von Neumann/Morgenstern characteristic function

In this work we examine the relationship between axiomatic structure and the classical derivation of a von Neumann⧸Morgenstern characteristic function for an N-person game. We show that it is possible to construct a von Neumann⧸Morgenstern characteristic function from weaker assumptions on the preference ordering on a mixture space that is generated by rational probabilities only. Within this weaker framework, we prove an analog of the classical representation result for von Neumann⧸Morgenstern characteristic functions derived from measurable utilities first proved by Luce and Adams in 1957.     

Partitioned matrices and Seidel convergence

Summary Without using spectral resolution, an elementary proof of convergence of Seidel iteration. The proof is based on the lemma (generalizing a lemma of P. Stein): If (A+A ^*)–B ^*(A+A ^*)B>0, whereB=–(P+L) ^–1 R,A=P+L (Lower)+R (upper), then Seidel iteration ofAX=Y ₀ converges if and only ifA+A ^*>0. This lemma has as corollaries not only the well-known results of E. Reich and Stein, but also applications to a matrix that can be far from symmetric, e.g.M=[A _ij ] ₁ ² , whereA ₂₁=–A ₁₂ ^* ,A ₁₁,A ₂₂ are invertible;A ₁₁ +A ₁₁ ^* =A₂₂+A ₂₂ ^* ; and the proper values ofA ₁₂ ^–1 A ₁₁,A ₁₂ ^*–1 A ₂₂ are in the interior of the unit disk.Supported under NSF GP 32527.Supported under NSF GP 8758.     

Population dynamics with infinite Leslie matrices: finite time properties

Infinite Leslie matrices, introduced by Demetrius 40 years ago, are mathematical models of age-structured populations defined by a countable infinite number of age classes. This article is concerned with determining solutions of the discrete dynamical system in finite time. We address this problem by appealing to the concept of kneading matrices and kneading determinants. Our analysis is applicable not only to populations models, but also to models of self-reproducing machines and self-reproducing computer programs. The dynamics of these systems can also be described in terms of infinite Leslie matrices.     

Absolutely bounded matrices and unconditional convergence

We characterize the so-called absolutely bounded matrices in terms of the (strong) unconditional convergence of their standard decompositions. There is a similar characterization of absolutely compact matrices, and both characterizations are closely related to some natural multiplication operators. Rudiments of the duality theory for the algebra of all absolutely bounded matrices are included.

     

An alternate relaxation approximation to conservation laws

In this paper we introduce a slight modification to the relaxation system of Jin and Xin which approximates a conservation law. The proposed alternate system satisfies an integral constraint that is more consistent than the standard one while retaining the semilinear structure. We establish L^∞$L^{\infty }$ estimates under the usual subcharacteristic condition and also construct a convex entropy.     

Exponential convergence of products of stochastic matrices

This paper considers a finite set of stochastic matrices of finite order. Conditions are given under which any product of matrices from this set converges to a constant stochastic matrix. Also, it is shown that the convergence is exponentially fast.     

A piecewise polynomial approach to analyzing interpolatory subdivision

The four-point interpolatory subdivision scheme of Dubuc and its generalizations to irregularly spaced data studied by Warren and by Daubechies, Guskov, and Sweldens are based on fitting cubic polynomials locally. In this paper, we analyze the convergence of the scheme by viewing the limit function as the limit of piecewise cubic functions arising from the scheme. This allows us to recover the regularity results of Daubechies et al. in a simpler way and to obtain the approximation order of the scheme and its first derivative.     

A tournament approach to pattern avoiding matrices

We consider the following Turán-type problem: given a fixed tournament H, what is the least integer t = t(n,H) so that adding t edges to any n-vertex tournament, results in a digraph containing a copy of H. Similarly, what is the least integer t = t(T _n ,H) so that adding t edges to the n-vertex transitive tournament, results in a digraph containing a copy of H. Besides proving several results on these problems, our main contributions are the following:

• Pach and Tardos conjectured that if M is an acyclic 0/1 matrix, then any n × n matrix with n(log n) ^O(1) entries equal to 1 contains the pattern M. We show that this conjecture is equivalent to the assertion that t(T _n ,H) = n(log n) ^O(1) if and only if H belongs to a certain (natural) family of tournaments.
• We propose an approach for determining if t(n,H) = n(log n) ^O(1). This approach combines expansion in sparse graphs, together with certain structural characterizations of H-free tournaments. Our result opens the door for using structural graph theoretic tools in order to settle the Pach–Tardos conjecture.

     

Quadratic convergence of scaled matrices in Jacobi method

Summary. A quadratic convergence bound for scaled Jacobi iterates is proved provided the initial symmetric positive definite matrix has simple eigenvalues. The bound is expressed in terms of the off-norm of the scaled initial matrix and the minimum relative gap in the spectrum. The obtained result can be used to predict the stopping moment in the two-sided and especially in the one-sided Jacobi method. Received October 31, 1997 / Revised version received March 8, 1999 / Published online July 12, 2000     

Poisson convergence of eigenvalues of circulant type matrices

We consider the point processes based on the eigenvalues of the reverse circulant, symmetric circulant and k-circulant matrices with i.i.d. entries and show that they converge to a Poisson random measures in vague topology. The joint convergence of upper ordered eigenvalues and their spacings follow from this. We extend these results partially to the situation where the entries are come from a two sided moving average process.     

On the convergence of powers of interval matrices

We give a necessary and sufficient condition for the sequence {$\text{A}$^k}of the powers of an interval matrix $\text{A}$ to converge to the null matrix $\text{O}$. We construct a point matrix $\text{B}$ which has spectral radius ? ($\text{B}$) less than one if {$\text{A}$^k}converges.     

Fractions continues de matrices,convergence et applications

The aim of this article is to give some property of continued fraction with matrices arguments, about their convergence and others applications. At the end of this work, we present a resolution of the Algebraic Riccati Equation by giving an explicit continued fraction development of its solution. This revised version was published online in August 2006 with corrections to the Cover Date.     

Displacement structure approach to Chebyshev-Vandermonde and related matrices

In this paper we use the displacement structure concept to introduce a new class of matrices, designated asChebyshev-Vandermonde-like matrices, generalizing ordinary Chebyshev-Vandermonde matrices, studied earlier by different authors. Among other results the displacement structure approach allows us to give a nice explanation for the form of the Gohberg-Olshevsky formulas for the inverses of ordinary Chebyshev-Vandermonde matrices. Furthermore, the fact that the displacement structure is inherited by Schur complements leads to a fastO(n ²) implementation of Gaussian elimination withpartial pivoting for Chebyshev-Vandermonde-like matrices.     

Additive mappings that do not increase minimal rank of alternate matrices

Additive mappings, which do not increase the minimal rank of alternate matrices, are completely classified. No condition is imposed on the underlying field.     

Additive mappings that do not increase minimal rank of alternate matrices

Additive mappings, which do not increase the minimal rank of alternate matrices, are completely classified. No condition is imposed on the underlying field.