An algebraic multigrid method with interpolation reproducing rigid body modes for semi-definite problems in two-dimensional linear elasticity

Based on the geometric grid information as geometric coordinates, an algebraic multigrid (AMG) method with the interpolation reproducing the rigid body modes (namely the kernel elements of semi-definite operator arising from linear elasticity) is constructed, and such method is applied to the linear elasticity problems with a traction free boundary condition and crystal problems with free boundary conditions as well. The results of various numerical experiments in two dimensions are presented. It is shown from the numerical results that the constructed AMG method is robust and efficient for such semi-definite problems, and the convergence is uniformly bounded away from one independent of the problem size. Furthermore, the AMG method proposed in this paper has better convergence rate than the commonly used AMG methods. Simultaneously, an AMG method that can preserve the quotient space, which means that if the exact solution of original problem belongs to the quotient space of discrete operator considered, then the numerical solution of AMG method is convergent in the same quotient space, is obtained using the technique of orthogonal decomposition.     

An MPEC formulation and its cutting constraint algorithm for continuous network design problem with multi-user classes

Continuous network design problem (CNDP) is to determine the set of link capacity expansions and the corresponding equilibrium flows for which the measures of performance index for the network is optimal. Conventionally, CNDP assumed users to be homogeneous, that is, all travelers on the same link of the network are identical insofar as congestion effect and they have the same value of time (VOT). In fact, it does not accord with the real situation that all have the same VOT. So, multiple user classes with different VOT should be considered. This paper examines the CNDP with different VOT for multiple user classes, which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). Then, the cut constraint algorithm (CCA) is presented to solve the problem. The numerical experiments on the examples from the literature are illustrated to demonstrate that our model and algorithm are feasible.     

An algorithm for the zeros of transcendental functions

Summary In this paper, we extend the dual form of the generalized algorithm of Sebastião e Silva [3] for polynomial zeros and show that it is effective for finding zeros of transcendental functions in a circle of analyticity.     

改进的带驻留时间隐Markov模型的前向-后向算法

对隐Maxkov模型(hidden Markov model:HMM)的状态驻留时间的概率进行了修订,给出了改进的带驻留时间隐Markov模型的结构,并在传统的隐Markov模型(traditional hidden Markov model:THMM)的基础上讨论了新模型的前向.后向变量,导出了新模型的前向-后向算法的迭代公式,同时也给出了新模型各个参数的重估公式.     

A global optimization algorithm for reliable network design

In this paper, we consider the problem of designing reliable networks that satisfy supply/demand, flow balance, and capacity constraints, while simultaneously allocating certain resources to mitigate the arc failure probabilities in such a manner as to minimize the total cost of network design and resource allocation. The resulting model formulation is a nonconvex mixed-integer 0-1 program, for which a tight linear programming relaxation is derived using RLT-based variable substitution strategies and a polyhedral outer-approximation technique. This LP relaxation is subsequently embedded within a specialized branch-and-bound procedure, and the proposed approach is proven to converge to a global optimum. Various alternative partitioning strategies that could potentially be employed in the context of this branch-and-bound framework, while preserving the theoretical convergence property, are also explored. Computational results are reported for a hypothetical scenario based on different parameter inputs and alternative branching strategies. Related optimization models that conform to the same class of problems are also briefly presented.     

基于参数设计的信噪比交叉效率评价方法

针对DEA交叉效率评价过程中没有考虑自评与互评效率的作用而主观赋予相同权重导致交叉效率评价值不准确的问题.文章基于参数设计的思想,依据试验设计中可控与不可控因素的作用机理区分自评权重和互评权重对所评价决策单元交叉效率的影响与作用,将其界定为可控与不可控因素的管理学属性,明确不同权重作用机理;引入信噪比作为衡量决策单元交...     

An effective algorithm for generation of factorial designs with generalized minimum aberration

Fractional factorial designs are popular and widely used for industrial experiments. Generalized minimum aberration is an important criterion recently proposed for both regular and non-regular designs. This paper provides a formal optimization treatment on optimal designs with generalized minimum aberration. New lower bounds and optimality results are developed for resolution-III designs. Based on these results, an effective computer search algorithm is provided for sub-design selection, and new optimal designs are reported.     

An integrated FMS design procedure

This paper considers the problem of the design of an FMS system. An integrated design procedure is outlined, which involves three stages — planning, design and implementation. Within each stage the design decisions to be made are discussed, together with the techniques and skills required to complete each design stage. At each stage, reference is made to the views of other designers and researchers. Finally, the procedure is illustrated through a case study of a miniature FMS designed and installed at the Cranfield Institute of Technology.     

Homotopy algorithm for symmetric eigenvalue problems

Summary The homotopy method can be used to solve eigenvalue-eigenvector problems. The purpose of this paper is to report the numerical experience of the homotopy method of computing eigenpairs for real symmetric tridiagonal matrices together with a couple of new theoretical results. In practice, it is rerely of any interest to compute all the eigenvalues. The homotopy method, having the order preserving property, can provide any specific eigenvalue without calculating any other eigenvalues. Besides this advantage, we note that the homotopy algorithm is to a large degree a parallel algorithm. Numerical experimentation shows that the homotopy method can be very efficient especially for graded matrices.Research was supported in part by NSF under Grant DMS-8701349     

An algorithm for a linear diophantine equation and a problem of Frobenius

Summary We solve the diophantine equation for nonnegative variablesx _j , wherea _j andL are positive integers. We characterize both the values ofL that lead to solutions and those that do not lead to solutions. We solve the Frobenius problem of finding the largest value ofL for which no solution exists.     

A nonparametric variable step-size NLMS algorithm for transversal filters

A nonparametric adaptive filtering approach is proposed in this paper. The algorithm is obtained by exploiting a time-varying step size in the traditional NLMS weight update equation. The step size is adjusted according to the square of a time-averaging estimate of the autocorrelation of a priori and a posteriori error. Therefore, the new algorithm has more effective sense proximity to the optimum solution independent of uncorrelated measurement noise. Moreover, this algorithm has fast convergence at the early stages of adaptation and small final misadjustment at steady-state process. It works reliably and is easy to implement since the update function is nonparametric. Furthermore, the experimental results in system identification applications are presented to illustrate the principle and efficiency of the proposed algorithm.     

An algorithm for the fast solution of symmetric linear complementarity problems

This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American options pricing. The paper proposes an improvement of a method described by Kocvara and Zowe (Numer Math 68:95–106, 1994) that combines projected Gauss–Seidel iterations with subspace minimization steps. The proposed algorithm employs a recursive subspace minimization designed to handle severely ill-conditioned problems. Numerical tests indicate that the approach is more efficient than interior-point and gradient projection methods on some physical simulation problems that arise in computer game scenarios. The research of J. L. Morales was supported by Asociación Mexicana de Cultura AC and CONACyT-NSF grant J110.388/2006. The research of J. Nocedal was supported by National Science Foundation grant CCF-0514772, Department of Energy grant DE-FG02-87ER25047-A004 and a grant from the Intel Corporation.     

An algorithm for a special case of a generalization of the Richardson extrapolation process

Summary A special case of a generalization of the Richardson extrapolation process is considered, and its complete solution is given in closed form. Using this, an algorithm for implementing the extrapolation is devised. It is shown that this algorithm needs a very small amount of arithmetic operations and very little storage. Convergence and stability properties for some cases are also considered.     

求鳞状循环因子矩阵的极小多项式的算法

提出了任意域上鳞状循环因子矩阵 ,利用多项式环的理想的Go bner基的算法给出了任意域上鳞状循环因子矩阵的极小多项式和公共极小多项式的一种算法 .同时给出了这类矩阵逆矩阵的一种求法 .在有理数域或模素数剩余类域上 ,这一算法可由代数系统软件Co CoA4 .0实现 .数值例子说明了算法的有效性     

An improved randomized approximation algorithm for maximum triangle packing

This paper deals with the maximum triangle packing problem. For this problem, Hassin and Rubinstein gave a randomized polynomial-time approximation algorithm that achieves an expected ratio of for any constant ?>0. By modifying their algorithm, we obtain a new randomized polynomial-time approximation algorithm for the problem which achieves an expected ratio of 0.5257(1−?) for any constant ?>0.     

A particle swarm algorithm for inspection optimization in serial multi-stage processes

Implementing efficient inspection policies is much important for the organizations to reduce quality related costs. In this paper, a particle swarm optimization (PSO) algorithm is proposed to determine the optimal inspection policy in serial multi-stage processes. The policy consists of three decision parameters to be optimized; i.e. the stages in which inspection occurs, tolerance of inspection, and size of sample to inspect. Total inspection cost is adopted as the performance measure of the algorithm. A numerical example is investigated in two phases, i.e. fixed sample size and sample size as a decision parameter, to ensure the practicality and validity of the proposed PSO algorithm. It is shown that PSO gives better results in comparison with two other algorithms proposed by earlier works.     

一种快速计算Zpk上码字深度的算法

开始定义了环Zpk上码字的深度,给出了一种快速计算环Zpk上码字的深度的算法.