线性规划问题的一种求解算法

本通过初等变换，并剔除常变量和零变量而对所给的线性规划问题进行预处理，得到的等价问题不仅易找初始可行基且初始可行解较优，易差别无可行解情形，而且可能使所含方程个数与变量个数减少，从而减少了求解问题的计算量和迭代次数。     

Fredholmness of Linear Combinations of Two Idempotents

Let E and F be idempotent operators on a complex Hilbert space, and let a and b be nonzero scalars with a + b ≠ 0. We prove that aE + bF is Fredholm if and only if E + F is, thus answering affirmatively a question asked by Koliha and Rakočević.      

m次数量幂等矩阵线性组合的可逆性

如果有非零数λ与μ使Pm=λP,Qm=μQ,则称P,Q分别是由λ,μ确定的m次数量幂等矩阵．本文证明了,若有非零数a与b,当μam-1（-1）m-1μbm-1≠0时,使可交换的分别由λ,μ确定的m次数量幂等矩阵P,Q的线性组合aP＋bQ是可逆的,那么对任意非零数u,u,当λμm-1-（-1）m-1μvm-1≠0时,uP＋vQ也是可逆的．本文主要结果和方法的应用,可以推广已有文献的2次、3次幂等矩阵的线性组合可逆的结论．     

反幂等阵线性组合的反幂等性

讨论了反幂等阵线性组合的幂等性,指出可对角化矩阵可表示为反幂等阵的线性组合,并由此得到了由非奇异矩阵构造两两正交且可交换的反幂等阵的一种方法.     

Merging of Linear Combinations to Semistable Laws

We prove merge theorems along the entire sequence of natural numbers for the distribution functions of suitably centered and normed linear combinations of independent and identically distributed random variables from the domain of geometric partial attraction of any non-normal semistable law. Surprisingly, for some sequences of linear combinations, not too far from those with equal weights, the merge theorems reduce to ordinary asymptotic distributions with semistable limits. The proofs require working out general conditions for merging in terms of characteristic functions.     

Linear Combinations of Generalized Crank Nicolson Schemes

The combination of two or more generalized Crank Nicolson schemesin order to obtain second, third and fourth order accurate discretizationsin time is considered. Particular attention is given to thestability properties of the methods proposed.     

An Algorithm for Approximate Multiparametric Linear Programming

Multiparametric programming considers optimization problems where the data are functions of a parameter vector and describes the optimal value and an optimizer as explicit functions of the parameters. In this paper, we consider a linear program where the right-hand side is an affine function of a parameter vector; we propose an algorithm for approximating its solution. Given a full-dimensional simplex in the parameter space and an optimizer for each simplex vertex, the algorithm formulates the linear interpolation of the given solutions as an explicit function of the parameters, giving a primal feasible approximation of an optimizer inside the simplex. If the resulting absolute error in the objective exceeds a prescribed tolerance, then the algorithm subdivides the simplex into smaller simplices where it applies recursively. We propose both a basic version and a refined version of the algorithm. The basic version is polynomial in the output size, provided a polynomial LP solver is used; the refined version may give a smaller output. A global error bound for the optimizer is derived and some computational tests are discussed.     

幂等算子线性组合的幂等性

设P与Q是Hilbert空间中的两个不同的幂等算子.本文主要刻画了幂等算子P与Q的线性组合仍是幂等算子的充要条件,从而推广了Baksalary与Baksalary (2000)的结论.值得指出的是,我们通过严密的推理发现,其定理的条件P_1P_2≠P_2P_1是非必要的.     

Bernstein-Type Inequalities for Linear Combinations of Shifted Gaussians

Let P_n be the collection of all polynomials of degree at mostn with real coefficients. A subtle Bernstein-type extremal problemis solved by establishing the inequality for all , and m= 1, 2, ..., where c is an absolute constant and Some related inequalities and direct and inversetheorems about the approximation by elements of in L_q (R) are also discussed. 2000 Mathematics SubjectClassification 41A17 (primary).     

Baskakov算子线性组合的点态估计

本文利用Ditizian-Totik模给出Baskakov算子线性组合点态和整体逼近正逆定理的统一形式,得到了较高的逼近阶,并且刻画了该线性组合算子的逼近特征。     

Pointwise Estimate for Linear Combinations of Bernstein-Kantorovich Operators

For linear combinations of Bernstein-Kantorovich operators K_n, r(f, x), we give an equivalent theorem with ω^2r_?^λ(f, t). The theorem unites the corresponding results of classical and Ditzian-Totik moduli of smoothness.     

On Convolutions and Linear Combinations of Pseudo-Isotropic Distributions

Let E be a Banach space, and let E* be its dual. For understanding the main results of this paper it is enough to consider E= ⁿ . A symmetric random vector X taking values in E is called pseudo-isotropic if all its one-dimensional projections have identical distributions up to a scale parameter, i.e., for every E* there exists a positive constant c() such that (, X) has the same distribution as c() X ₀, where X ₀ is a fixed nondegenerate symmetric random variable. The function c defines a quasi-norm on E*. Symmetric Gaussian random vectors and symmetric stable random vectors are the best known examples of pseudo-isotropic vectors. Another well known example is a family of elliptically contoured vectors which are defined as pseudo-isotropic with the quasi-norm c being a norm given by an inner product on E*. We show that if X and Y are independent, pseudo-isotropic and such that X+Y is also pseudo-isotropic, then either X and Y are both symmetric -stable, for some (0, 2], or they define the same quasi-norm c on E*. The result seems to be especially natural when restricted to elliptically contoured random vectors, namely: if X and Y are symmetric, elliptically contoured and such that X+Y is also elliptically contoured, then either X and Y are both symmetric Gaussian, or their densities have the same level curves. However, even in this simpler form, this theorem has not been proven earlier. Our proof is based upon investigation of the following functional equation:

Random Linear Combinations of Functions from L 1

In this paper, properties of random polynomials with respect to a general system of functions are studied. Some lower bounds for the mathematical expectation of the uniform norm and the recently introduced integral-uniform norm of random polynomials are established.     

On Wait-and-See Stochastic Linear Programmes: An Application and an Algorithm

This paper develops a computational algorithm for estimating the mean objective function value of a stochastic linear programming problem of the passive or wait-and-see type. The algorithm is applied to a problem connected with design of a milk-grid in India and is found to be computationally effective in that case. It is most likely to be useful in the case of fairly large LP problems with a few (<10) stochastic right hand side variables.     

Pointwise Estimates for Linear Combinations of Gamma Operators

For linear combinations of Gamma operators G_n,r(f,x), we give an equivalent theorem with (f,t), where (f,t) are the Ditzian-Totik moduli of smoothness ( ).AMS Subject Classification (1991): 41A25, 41A36.Supported by NSF of Hebei ProvinceSupported by NSF of Hebei Province     

线性分式运输问题的一个解法

线性分式运输问题是线性分式规划问题的一种特殊情况，通常可以用线性分式规划问题的一般解法来解这类问题，本文针对分式运输问题的特点给出了一种简便的解法．     

求解二层线性规划问题的一种算法

对下层含有约束的二层线性规划问题,提出了求全局最优解的一种算法.首先由该算法求出约束凸集的全部极点,再对极点进行可行性检验,从而得到了二层线性规划问题的全局最优解,最后以实例验证了算法的有效性.     

一种改进的双层规划内点算法(英文)

本文针对线性双层规划问题提出一个由KMY算法演变而来的原对偶内点算法.与现在很多线性双层规划单纯型算法不同,作者提出的算法从一可行初始点穿过约束多面体内部直接得到近似最优解,当约束条件和变量数目增加时,本算法的迭代次数和计算时间变化很小.所以大大提高实际可操作性能和运算效率.     

An Algorithm for Solving Mixed Integer Linear Programmes

A simplified form of an algorithm for solving mixed integer linear programmes is presented. It is introduced by considering the geometry of the problem, from which most of the terminology originates. The ideas developed are then translated into algebra. A simple logical flow diagram is presented and its use illustrated by a worked example. An appendix covers the more important refinements.     

数量对合矩阵的线性组合的秩的不变性

若矩阵A、B满足A2=λ2I、B2=μ2I（λμ≠0）,称A、B都是数量对合矩阵．当非零复数a、b、u、v满足μλ＋bμ≠0、uλ＋vμ≠0时,我们证明了数量对合矩阵A、B与单位矩阵,的线性组合的秩总是相等,并且是一个与a、b、札、u选择都无关的常数．应用所得到数量对合矩阵的线性组合的秩的不变性,可推广已有文献的关于对合矩阵的相应结果．