A technique to construct symmetric variable-stepsize linear multistep methods for second-order systems

Some previous works show that symmetric fixed- and variable-stepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts, in such a way that the former have the same order as the latter. The order and symmetry of the integrators obtained is proved independently of the order of the underlying fixed-stepsize integrators. As this technique looks for efficiency, we concentrate on explicit linear multistep methods, which just make one function evaluation per step, and we offer some numerical comparisons with other one-step adaptive methods which also show a good long-term behaviour.

     

On quasi-solution to infeasible linear complementarity problem obtained by Lemke’s method

For a linear complementarity problem with inconsistent system of constraints a notion of quasi-solution of Tschebyshev type is introduced. It’s shown that this solution can be obtained automatically by Lemke’s method if the constraint matrix of the original problem is copositive plus or belongs to the intersection of matrix classes P ₀ and Q ₀.     

On the advantage over a random assignment

We initiate the study of a new measure of approximation. This measure compares the performance of an approximation algorithm to the random assignment algorithm. This is a useful measure for optimization problems where the random assignment algorithm is known to give essentially the best possible polynomial time approximation. In this paper, we focus on this measure for the optimization problems Max‐Lin‐2 in which we need to maximize the number of satisfied linear equations in a system of linear equations modulo 2, and Max‐k‐Lin‐2, a special case of the above problem in which each equation has at most k variables. The main techniques we use, in our approximation algorithms and inapproximability results for this measure, are from Fourier analysis and derandomization. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

一般线性模型下方差最小范数二次无偏估计的稳健性

本文给出了一般线性模型下,由最小二乘得到的方差估计与最小范数二次无偏估计相等的充分必要条件,并且当Gauss-Markov估计与最小二乘估计相等时,可以得到一个简单的等价条件。     

广义线性模型(六)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 :建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的 :《MultivariateStatisticalModel ingBasedonGeneralizedLinearModles》。     

基于改进的语音参数提取的线性预测

根据语音发生基本原理和线性预测编码原理，针对自相关法需要加窗从而降低了解的精度，而协方差法不能保证保证解所重构出系统的稳定性的特点，提出了一种改进的Cholesky分解的方法求解协方差方程组以产生声道模型参数的方法，实践证明，这种方法既保证了系统的稳定性，又提高了解的精度。     

New Branch-and-Cut Algorithm for Bilevel Linear Programming

Linear mixed 0–1 integer programming problems may be reformulated as equivalent continuous bilevel linear programming (BLP) problems. We exploit these equivalences to transpose the concept of mixed 0–1 Gomory cuts to BLP. The first phase of our new algorithm generates Gomory-like cuts. The second phase consists of a branch-and-bound procedure to ensure finite termination with a global optimal solution. Different features of the algorithm, in particular, the cut selection and branching criteria are studied in details. We propose also a set of algorithmic tests and procedures to improve the method. Finally, we illustrate the performance through numerical experiments. Our algorithm outperforms pure branch-and-bound when tested on a series of randomly generated problems. Work of the authors was partially supported by FCAR, MITACS and NSERC grants.     

高阶线性微分方程的解及其解的导数的不动点

研究了复域齐次和非齐次线性微分方程的解及其解的导数的不动点与超级问题,得到了整函数系数的齐次和非齐次线性微分方程的解及其解的导数的不动点的两个结果,所得结果推广了一些相关结果.     

Cauchy problem in the class of monotone increasing functions

The paper establishes some solvability conditions of the Cauchy problem for linear differential equation in the class of monotone increasing functions. The results are applied for clarifying the possibility of flight along a given trajectory under existence of braking forces.     

A solution procedure for the discrete time, cost and quality tradeoff problem using electromagnetic scatter search

Decisions concerning a project’s expedition, traditionally involved considerations regarding time and cost tradeoff. It was recently suggested that the quality of a project should also be taken into considerations. In this paper, we propose a meta-heuristic solution procedure for the discrete time, cost and quality tradeoff problem. This problem involves the scheduling of project activities in order to minimize the total cost of the project while maximizing the quality of the project and also meeting a given deadline. We apply a so called electromagnetic scatter search to solve this problem. In this process, we initially generate a population of feasible solutions. In so doing, we use frequency memory to well sample the feasible region. A number of these solutions are then selected and improved locally. The improved solutions are then combined to generate new set of solutions. The combination process utilizes attraction–repulsion mechanisms borrowed from the electromagnetism theory. The whole process is stopped when no significant improvement in the set of solutions are observed. The validity of the proposed solution procedure is demonstrated, and its applicability is tested on a randomly generated large and complex problem having 19,900 activities.