Symmetric multivariate orthogonal refinable functions

In this paper, we shall investigate the symmetry property of a multivariate orthogonal M-refinable function with a general dilation matrix M. For an orthogonal M-refinable function such that is symmetric about a point (centro-symmetric) and provides the approximation order k, we show that must be an orthogonal M-refinable function that generates a generalized coiflet of order k. Next, we show that there does not exist a real-valued compactly supported orthogonal 2I_s-refinable function in any dimension such that is symmetric about a point and generates a classical coiflet. Finally, we prove that if a real-valued compactly supported orthogonal dyadic refinable function L₂(R^s) has the axis symmetry, then cannot be a continuous function and can provide the approximation order at most one. The results in this paper may provide a better picture about symmetric multivariate orthogonal refinable functions. In particular, one of the results in this paper settles a conjecture in [D. Stanhill, Y.Y. Zeevi, IEEE Trans. Signal Process. 46 (1998), 183–190] about symmetric orthogonal dyadic refinable functions.     

The curvature integral and the complexity of linear complementarity problems

In this paper, we propose a predictor—corrector-type algorithm for solving the linear complementarity problem (LCP), and prove that the actual number of iterations needed by the algorithm is bounded from above and from below by a curvature integral along the central trajectory of the problem. This curvature integral is not greater than, and possibly smaller than, the best upper bound obtained in the literature to date.Corresponding author.This author's research was partially supported by Research Grant No. RP920068, National University of Singapore, Singapore.     

算子值加权模式在Banach空间的实现理论

本文处理能在Ｂａｎａｃｈ空间中实现的线性连续时间系统．这里，输入、输出和状态空间都是无穷维Ｂａｎａｃｈ空间．我们证明：加权模式有Ｂａｎａｃｈ空间实现的充要条件是它强连续且为指数阶．对状态算子是解析半群的无穷小生成元的情况，得到了Ｂａｎａｃｈ空间实现的存在性定理．所有定理都是在时间域中给出的．     

光学非线性薄膜线性参数的快速测量与分析

本文提出了-种光学非线性薄膜线性参数的方便有效的测量方法,测量了ZnSe非晶态光学薄膜的线性折射率和消光系数。在此方法中,实验数据的计算与处理由-套计算机软件来完成。最后,文章对测量精度进行了简单的讨论。     

Linear programming with online learning

We propose online decision strategies for time-dependent sequences of linear programs which use no distributional and minimal geometric assumptions about the data. These strategies are obtained through Vovk's aggregating algorithm which combines recommendations from a given strategy pool. We establish an average-performance bound for the resulting solution sequence.     

双字节整数插值计算的精度分析及其应用

在微机测控系统和智能仪器仪表中,常用线性插值法实现传感器静态误差校正和函数逼近计算等。本文分析了用双字节定点整数运算进行插值计算所能达到的计算精度,并列举了两个计算实例。分析和计算结果证明:只要对原始数据进行合理的量化处理,双字节整数插值计算可以达到10~(-4)～10~(-5)数量级的精度。因此,这种算法可以广泛应用于微机化的系统和仪器中。采用较短字长的整数运算,具有实时性好,要求存贮器容量小和程序简单等三个突出的优点。     

New crash procedures for large systems of linear constraints

Many algorithms for solving linearly constrained optimization problems maintain sets of basic variables. The calculation of the initial basis is of great importance as it determines to a large extent the amount of computation that will then be required to solve the problem. In this paper, we suggest a number of simple methods for obtaining an initial basis and perform tests to indicate how they perform on a variety of real-life problems.     

Eliminating columns in the simplex method for linear programming

We propose a column-eliminating technique for the simplex method of linear programming. A pricing criterion is developed for checking whether a dual hyperplane corresponding to a column intersects a simplex containing all of the optimal dual feasible solutions. If the dual hyperplane has no intersection with this simplex, we can eliminate the corresponding column from further computation during the course of the simplex method.The author is grateful for many discussions with Professor G. B. Dantzig, Stanford University, and for his valuable suggestions about this work. The author also gratefully acknowledges the editor and two referees for their very helpful comments, corrections, and remarks.     

一种新的线性规划多项式时间算法

本文给出了一种新的线性规划多项式时间算法。在此算法中，每步可沿一族方向中的一个进行线性搜索，同时，还使用了开关策略，从而大大减少了求逆矩阵的次数，最后，证明了算法经Ｏ（ｎＬ）次迭代结束。     

ASYMPTOTICALLY OPTIMAL SUCCESSIVE OVERRELAXATION METHODS FOR SYSTEMS OF LINEAR EQUATIONS

We present a class of asymptotically optimal successive overrelaxation methods for solving the large sparse system of linear equations. Numerical computations show that these new methods are more efficient and robust than the classical successive overrelaxation method.