可视球面多分辨率网格建模与求解

针对任意视点下的球面多分辨率网格建模与求解困难的情况,提出了屏幕细分自适应算法.该算法将计算限制在与视点相关的可视球面区域,求解得到视点相关的可视球面多分辨率网格,并在PC机上实现了可视球面多分辨率网格的三维表现.     

基于多分辨率分析的股票市场预测模型研究

采用多分辨率分析技术将深证成指收盘数据序列分解为多个子序列,然后采用神经网络技术对每个子序列分别建立预测模型,将各个预测结果叠加后得到最终预测结果.研究首先发现多分辨率技术可以有效提高预测模型的预测精度,表明分析我国股市波动时应该按照不同因素对股市影响大小及周期的差异分别研究,才能更有效分析股市运行状况及对其预测;其次结果表明不同类型神经网络预测模型预测性能差异明显,在选择股市预测模型的神经网络类型时应该注意其学习算法及收敛过程,以便能更好捕获股市变化规律.     

广义多值拟变分包含解的两步迭代

本文引入并研究了Hilbert空间中的一类广义多值拟变分包含问题.借助预解算子技巧构造了一个新的两步迭代算法来逼近广义多值拟变分包含的解,并且证明了其解的存在性以及迭代算法生成的迭代序列的收敛性.     

多行程车辆路径问题中变邻域搜索算法的应用

多行程车辆路径问题是标准车辆路径问题的一个变体,每个车辆在运行期间可以使用不止一次.对于这种NP-HARD问题,提出了一个改进变邻域搜索算法并设计了四个邻域结构用于求解和制定多行程路径问题的调度规划.算法测试了一组标准实例问题,获得的解决方法与文献中提出的三种不同数据集进行比较计算证明,算法提供了较高质量的求解结果.最后采用三个标准函数进行数值计算,与PSO和GA算法进行比较证明,提出的VNS算法虽然运行花费时间较长,但是达到全局收敛性的比率和全局收敛性都远超其他两种算法.     

一类求解双边障碍问题的松弛型二级多分裂并行算法

本文研究了一类求解双障碍问题的松弛型二级多分裂并行算法.运用矩阵多分裂理论,在一定条件下证明了算法的收敛性.数值算例说明算法是有效的和稳健的.     

非对称线性互补问题的并行二级多分裂迭代法

提出了求解非对称线性互补问题的并行二级多分裂迭代算法,并证明了该算法的收敛性,最后通过数值实验验证了算法的有效性和可行性.     

一种求解单调变分不等式的部分并行分裂LQP交替方向法

LQP交替方向法是求解可分离结构型单调变分不等式问题的一种非常有效的方法.它不仅可以充分地利用目标函数的可分结构,将原问题分解为多个更易求解的子问题,还更适合求解大规模问题.对于带有三个可分离算子的单调变分不等式问题,结合增广拉格朗日算法和LQP交替方向法提出了一种部分并行分裂LQP交替方向法,构造了新算法的两个下降方向,结合这两个下降方向得到了一个新的下降方向,沿着这个新的下降方向给出了最优步长.并在较弱的假设条件下,证明了新算法的全局收敛性.     

复合材料特征值的高阶多尺度Rayleigh商校正

本文讨论了周期结构复合材料特征值的多尺度计算,提出了高阶多尺度Rayleigh商校正算法,并给出了收敛性分析. 最后,通过大量数值实验结果表明,新算法是有效且必要的.     

求解变分不等式的Ishikawa类迭代算法

本文讨论Banach空间中子集非紧的情况下的变分不等式数值解.提出了求解相应问题的Ishikawa类迭代算法,证明了算法的子列收敛性和全局收敛性.同时也证明了变分不等式解的存在性.     

三维复合介质波动方程多尺度辛几何算法

本文针对三维复合介质波动方程,提出了一类多尺度辛几何算法.其主要内容有:1.快速振荡系数三维波动方程的多尺度渐近分析与收敛性估计;2.均匀化波动方程的辛几何算法;3.多尺度辛几何算法与数值实验结果.     

Computation of interpolatory splines via triadic subdivision

We present an algorithm for the computation of interpolatory splines of arbitrary order at triadic rational points. The algorithm is based on triadic subdivision of splines. Explicit expressions for the subdivision symbols are established. These are rational functions. The computations are implemented by recursive filtering.     

Normal Multiresolution Approximation of Curves

A multiresolution analysis of a curve is normal if each wavelet detail vector with respect to a certain subdivision scheme lies in the local normal direction. In this paper we study properties such as regularity, convergence, and stability of a normal multiresolution analysis. In particular, we show that these properties critically depend on the underlying subdivision scheme and that, in general, the convergence of normal multiresolution approximations equals the convergence of the underlying subdivision scheme.     

A Unified Ternary Curve Subdivision Scheme

A unified $m\,(m>2)$-point ternary scheme with some parameter is proposed. The continuity of subdivision scheme is analyzed based on the relationship between the subdivision scheme and difference scheme. Moreover, the proposed subdivision is extended to asymmetric multi-parameter subdivision and the asymmetric schemes in four cases are presented in detail. Some examples are given to show that the presented scheme has better approximating effect.     

Regularity of multivariate vector subdivision schemes

In this paper we discuss methods for investigating the convergence of multivariate vector subdivision schemes and the regularity of the associated limit functions. Specifically, we consider difference vector subdivision schemes whose restricted contractivity determines the convergence of the original scheme and describes the connection between the regularity of the limit functions of the difference subdivision scheme and the original subdivision scheme.     

Error bounds for a convexity-preserving interpolation and its limit function

Error bounds between a nonlinear interpolation and the limit function of its associated subdivision scheme are estimated. The bounds can be evaluated without recursive subdivision. We show that this interpolation is convexity preserving, as its associated subdivision scheme. Finally, some numerical experiments are presented.     

基于逼近型细分的诱导细分格式

利用逼近型细分构造插值型细分是细分领域中的一个重要问题,目前可以给出插值型细分生成函数的研究还非常少.本文给出一个生成函数的统一公式,该公式由逼近型细分的生成函数与一个子生成函数构成.该公式对应一个插值型细分或者逼近型细分,这个取决于子生成函数的选取.该公式在理论和实际中都很重要.首先,这个公式适用于任意伸缩矩阵的多元基本型细分;其次,不论是一元细分还是多元细分,推导这个统一公式都不需要求解线性方程组;再次,这个公式具有显著的几何意义,应用方便;最后,从理论上分析诱导细分的零条件和多项式再生性,本文发现这些性质不仅与逼近型细分的零条件有关,而且与逼近型细分的多项式再生性有关,从而对细分格式的构造有指导意义.本文给出3个例子来说明这个统一公式.     

de Rham transforms for subdivision schemes

For any subdivision scheme, we define its de Rham transform, which generalizes the de Rham and Chaikin corner cutting. The main property of the de Rham transform is that it preserves a sum rule. This allows comparison of the Hölder regularity of a given subdivision scheme with that of its de Rham transform. A graphical comparison is made for three different families of subdivision schemes, the last one being the generalized four-point scheme.     

三进制Loop细分曲面的C~1连续性分析

本文利用计算机代数系统,通过对三进制Loop细分算法的细分矩阵和特征映射的构造与分析,证明Loop给出的掩模设计能够保证细分曲面在奇异点是C1连续的,还给出细分矩阵的次优势特征值的一个取值范围,在此范围内利用三进制Loop细分算法生成的细分曲面都是C1连续的.最后给出一种三进制Loop细分算法的新的边点掩模设计方法,在保证细分曲面是C1连续的前提下,比Loop给出的计算公式更简单,细分算法在奇异点附近收敛更快.     

Convergent Vector and Hermite Subdivision Schemes

Hermite subdivision schemes have been studied by Merrien, Dyn, and Levin and they appear to be very different from subdivision schemes analyzed before since the rules depend on the subdivision level. As suggested by Dyn and Levin, it is possible to transform the initial scheme into a uniform stationary vector subdivision scheme which can be handled more easily.With this transformation, the study of convergence of Hermite subdivision schemes is reduced to that of vector stationary subdivision schemes. We propose a first criterion for C⁰-convergence for a large class of vector subdivision schemes. This gives a criterion for C¹-convergence of Hermite subdivision schemes. It can be noticed that these schemes do not have to be interpolatory. We conclude by investigating spectral properties of Hermite schemes and other necessary/sufficient conditions of convergence.     

Scalar and Hermite subdivision schemes

A criterion of convergence for stationary nonuniform subdivision schemes is provided. For periodic subdivision schemes, this criterion is optimal and can be applied to Hermite subdivision schemes which are not necessarily interpolatory. For the Merrien family of Hermite subdivision schemes which involve two parameters, we are able to describe explicitly the values of the parameters for which the Hermite subdivision scheme is convergent.