An Algorithm for the Exact Numerical Integration of a Special Class of Functions

The classical Gaussian quadrature rules yield very inaccurate results when they are used for the integration of functions of the form f(x)=P(x,\cos(cx+d))\exp(-a^{2}x^{2}+bx) over the infinite interval (-\infty, \infty) , where a\gt 0, b, c, d are real numbers and P is a polynomial. In this paper we propose a new algorithm that computes this type of integrals without error in the machine precision. The algorithm can also be used for the multiple integrals. We give some numerical examples to compare the results obtained by the new algorithm and those obtained by some other methods including the classical Gauss-Hermite integration rules.     

Variational Methods for Normal Integration

The need for an efficient method of integration of a dense normal field is inspired by several computer vision tasks, such as shape-from-shading, photometric stereo, deflectometry. Inspired by edge-preserving methods from image processing, we study in this paper several variational approaches for normal integration, with a focus on non-rectangular domains, free boundary and depth discontinuities. We first introduce a new discretization for quadratic integration, which is designed to ensure both fast recovery and the ability to handle non-rectangular domains with a free boundary. Yet, with this solver, discontinuous surfaces can be handled only if the scene is first segmented into pieces without discontinuity. Hence, we then discuss several discontinuity-preserving strategies. Those inspired, respectively, by the Mumford–Shah segmentation method and by anisotropic diffusion, are shown to be the most effective for recovering discontinuities.     

A Universal Decomposition of the Integration Range for Exponential Functions

The problem of determining the independent constants for decomposition of the integration range of exponential functions was solved on the basis of a similar approach to polynomials. The constants obtained enable one to decompose the integration range in two so that the integrals over them are equal independently of the function parameters. For the nontrigonometrical polynomials of even functions, an alternative approach was presented.     

基于数值积分法的弹道导弹落点实时预测

为了及时准确预测洲际导弹再入段落点,直观、清晰地为靶场指控中心呈现落点偏差;以数值积分法为基础,通过使用光电经纬仪交会测量数据修正预测结果来排除扰动引力对预测结果的影响,实现对弹体落点的精确预测,并结合Direct3D图形编程技术设计落点预测模拟显示系统;实验结果表明:该方法预测误差≤50m,模拟目标运动过程逼真、平稳,落点显示直观,可作为操作人员的预判依据,满足了靶场测量过程中实时预测和显示弹体落点的要求。     

空间几何变换算法的可视化处理

给出物体空间坐标几何变换的常见算法,采用平移、缩放、旋转、投影等变换矩阵将抽象问题具体化为相关算法,并以可视化计算的方法,通过例程直现表现出这些算法对于简单构型物体的实现过程.所提出的可视化算法是面向对象的,具有很好的通用性.     

Quantum Coin Method for Numerical Integration

Light transport simulation in rendering is formulated as a numerical integration problem in each pixel, which is commonly estimated by Monte Carlo integration. Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e. samples) of the function (integrand). For N queries of the integrand, Monte Carlo integration achieves the estimation error of . Recently, Johnston [Joh16] introduced quantum super-sampling (QSS) into rendering as a numerical integration method that can run on quantum computers. QSS breaks the fundamental limitation of the convergence rate of Monte Carlo integration and achieves the faster convergence rate of approximately which is the best possible bound of any quantum algorithms we know today [NW99]. We introduce yet another quantum numerical integration algorithm, quantum coin (QCoin) [AW99], and provide numerical experiments that are unprecedented in the fields of both quantum computing and rendering. We show that QCoin's convergence rate is equivalent to QSS's. We additionally show that QCoin is fundamentally more robust under the presence of noise in actual quantum computers due to its simpler quantum circuit and the use of fewer qubits. Considering various aspects of quantum computers, we discuss how QCoin can be a more practical alternative to QSS if we were to run light transport simulation in quantum computers in the future.     

数值属性的离散方法研究

数值属性的离散化对于事务的构成有重要的意义，本文给出了数值属性的总体描述，并针对网络性能数据的离散化设计了多种方法。     

Splitting Methods for Three-Dimensional Transport Models with Interaction Terms

We investigate the use of splitting methods for the numerical integration of three-dimensional transport-chemistry models. In particular, we investigate various possibilities for the time discretization that can take advantage of the parallelization and vectorization facilities offered by multi-processor vector computers. To suppress wiggles in the numerical solution, we use third-order, upwind-biased discretization of the advection terms, resulting in a five-point coupling in each direction. As an alternative to the usual splitting functions, such as co-ordinate splitting or operator splitting, we consider a splitting function that is based on a three-coloured hopscotch-type splitting in the horizontal direction, whereas full coupling is retained in the vertical direction. Advantages of this splitting function are the easy application of domain decomposition techniques and unconditional stability in the vertical, which is an important property for transport in shallow water. The splitting method is obtained by combining the hopscotch-type splitting function with various second-order splitting formulae from the literature. Although some of the resulting methods are highly accurate, their stability behaviour (due to horizontal advection) is quite poor. Therefore we also discuss several new splitting formulae with the aim to improve the stability characteristics. It turns out that this is possible indeed, but the price to pay is a reduction of the accuracy. Therefore, such methods are to be preferred if accuracy is less crucial than stability; such a situation is frequently encountered in solving transport problems. As part of the project TRUST (Transport and Reactions Unified by Splitting Techniques), preliminary versions of the schemes are implemented on the Cray C98 4256 computer and are available for benchmarking.     

形式方法与面向对象方法的结合探讨

文中讨论了形式方法和面向对象方法各自的优缺点，结合作者设计的面向对象形式规格说明语言ＯＯＺＳ，介绍了将这两种方法结合起来的三种途径，并对这三种途径进行分析，评价和对比，最后提出了今后的研究方向。     

二维广义系统的实现方法

给出两种二维广义系统的实现方法，第一种方法是通过两次一维广义实现来完成一种特殊的广义Ｒｏｅｓｓｅｒ模型实现；第二种方法根据两个二维广义系统实现与它们的传递函数阵乘积的实现关系，把待实现的二维传函函数阵与写成容易实现的传递函数矩阵乘积的形式而得到原系统的实现。     

固体火箭冲压发动机三维数值计算

利用FLUENT中的概率密度函数非预混模型对固体火箭冲压发动机补燃室内的气相湍流燃烧进行数值模拟.主要目的是解决在固体火箭冲压发动机含镁铝推进剂的补燃室中,存在上百种中间及最终产物.复杂的反应机理使采用有限反应速率模型难以模拟补燃室中复杂的湍流燃烧的问题.模拟结果有助于提高对固体火箭冲压发动机补燃室内部流场流动的了解.模拟结果表明:补燃室内发生着复杂的三维化学反应流动,存在对掺混燃烧有重要影响的头部回流和轴向涡流.补燃室内温度分布与空气与燃气的掺混、燃烧及流动状态有密切关系.提高空燃比,可增强补燃室中燃气的回流和轴向涡流强度,加大掺混力度.提高燃烧效率.     

虚拟试验仪器及其类同功能集成

通过使用软件方法集成虚拟试验仪器和它们的类同功能,达到了便于操作、集中统一管理和方便维护的目的,提高了实验的效率.     

Error of Partitioned Runge-Kutta Methods for Multiple Stiff Singular Perturbation Problems

The main purpose of this paper is to deal with error behaviour of partitioned Runge-Kutta methods for one-parameter multiple stiff singular perturbation problems whose stiffness is caused by a small parameter ε and some other factors and to present some quantitative convergence results. Received November 30, 1998; revised August 10, 1999     

信息系统集成方法研究

随着信息源的不断增多,如何在多个信息系统中迅速查找用户感兴趣的信息越来越受到人们的关注。信息集成是指将多个信息源进行整合,并为用户提供一个统一的数据视图和访问接口。对信息系统的集成方法进行了研究,分析和比较了两种主要的信息集成方法:数据仓库方法和中介模式方法,并对未来的一些研究热点进行了前瞻。     

Computer-Aided Analysis of Transformation Formulas for Appel and Horn Functions

Simultaneous use of general and special linear transformations allows 36 transformations for the Appel function F ₄ to be obtained. This result is important because F ₄ is widely used in physics and mathematics. The transformations express F ₄ in terms of the Appel functions F ₁, F ₂, and F ₃; the Horn function H ₂; and non-Hornian series G, K, and . Until now, it was not possible to obtain linear multiplets having such a large dimensionality. A program based on Maple V4 was developed for formula generation. Details of program operation and possible applications of the results obtained are discussed.