二维经验模态分解边界效应抑制研究

二维经验模态分解中边界效应抑制是一个关键问题,现有方法主要讨论一维信号端点效应抑制,基本思想是信号延拓,不适合对二维信号进行边界效应抑制。提出一种二维图像边界效应抑制方法,该方法根据对称性、局部性原理和牛顿插值理论,对边界点进行插值,获取部分边界极值,采用这些极值对边界进行线性插值获取图像每个边界像素点的极大值和极小值。把这种边界效应抑制方法应用到二维经验模态分解中收到了较好的实验效果。     

基于互信息图像配准中的局部极值问题研究

基于互信息的图像配准方法具有自动化程度高、配准精度高等优点,近年来在医学图像配准中得到广泛应用。但是当变换后像素坐标位于非采样网格点时,插值算法有时会使目标函数产生局部极值,使得最优化搜索终止于局部极值,得到错误的配准结果。分析了两种常见的插值算法和产生局部极值的原因,在此基础上提出一种新的插值算法。实验结果表明,该算法有效地抑制了基于互信息的目标函数的局部极值问题,使目标函数更加平滑。     

一种新的光线空间插值方法研究

基于灰度共生矩阵的思想分析光线空间数据特征，在此基础上提出一种基于主方向匹配的光线空间插值方法。实验结果表明，新的插值方法插值生成的光线空间与传统的线性插值方法和自适应滤波插值方法生成的光线空间相比在PSNR上分别提高了3．44dB和1．97dB。     

空间散乱数据插值设计与实现

本文以一种新的思路提出Shepard与Clough-Tother结合使用的曲面插值方法.该方法利用模式识别中的K近邻法在Shepard插值的局部极值点处构造三角面片,用效果好的Clough-Tocher方法精化插值结果,提高了插值质量.实验结果表明本文提出的方法可以获得较高精度的曲面,方法简单,便于应用,弥补了传统插值算法的不足.     

基于多项式拟合算法的EMD端点问题的处理

经验模态分解(EMD)是由Huang等发展的一种新的数据分析方法,但是在利用样条插值获得上下包络过程中存在着棘手的端点问题。文章在解决该问题已有算法的基础上,提出了多项式拟合算法。它利用多项式来拟合临近端点处的极值点序列,再由此多项式求出极值点序列在端点处的近似取值,使得对极值点进行插值的三次样条在端点处不会发生大的摆动。通过对三种算法进行比较,证明了多项式拟合算法可以有效地抑制端点效应。     

一种应用于地球系统模式的通用插值算法模型

地球系统模式的现有插值算法误差较大、网格适用性差,无法满足其未来的发展需求。提出了一种插值算法分类方法,根据此方法设计了一个通用插值算法模型。该模型基于复合算法的思想,既可表示现有算法,还可通过选择适当的两个算法灵活构造出局部的高精度的新算法。根据此模型并利用径向基函数良好的插值效果提出了两个新的插值算法。基于球面Voronoi图的搜索算法可有效优化插值算法的实现。实验结果表明新算法具有良好的插值效果。     

基于张力格林样条的EMD均值曲线插值方法

经典经验模式分解采用三次样条插值方法求取信号的均值曲线,其存在较严重的过冲现象,造成最终的分解误差较大。针对上述问题,提出一种基于张力格林样条的均值曲线插值方法。以相邻极值点的中点为插值节点,采用张力格林样条插值直接获得信号的均值曲线。实验结果表明,该方法在保证插值曲线光滑性的基础上,可以消除三次样条在插值节点间出现的过分振荡现象,一定程度上克服过冲问题,基于极值中点的一次插值能进一步降低信号分解的误差。     

基于切向约束构造复合二次B样条插值曲线

该文提出一种构造二次B样条插值曲线的新方法,包括新的参数化方法和新的插值方法.新参数化方法中,相邻曲线段的连接处与插值点相一致,以插值点的切向作为约束,利用二次B样条曲线本身的几何性质进行参数化,使曲线在每个插值点上都满足指定的切向,可以直观地控制插值曲线的形状以达到预期效果,参数化方法稳定,不必解方程组.在新参数化方法的基础上进一步提出了分段构造的思想,将形状不好的段分成多段构造,除插值点的切向外还留有其他的自由度进一步直观调控曲线的形状,使得二次B样条插值曲线的形状更自然.新方法对于数据点的改变具有良好的局部性.实例表明该方法是有效的.     

仿真插值算法研究

一、引言求解时变系数的微分方程时,如果处理变系数采用的方法不当,会给最终结果带来不利的影响,这里考虑三种经典插值方法: 1.一次分段线性插值:快速,但不光滑 2.二次分段抛物插值:速度较慢,分段光滑,但节点处不光滑上述两种方法在极值(局部)情况下,处理结果不够理想     

基于动态双极值模糊软集的群决策方法

针对实际问题中双极值模糊软集随时间变化的影响，定义了动态双极值模糊软集等概念，讨论了相关运算及性质。根据时间权重符合对数增长模型得到权重确定公式。利用集成思想定义双极值模糊软集的运算并给出几何加权平均算子的计算公式，将动态双极值模糊软集集成为综合双极值模糊软集。利用水平软集算出各对象的机会值，得出最优决策。通过实例分析证明此决策方法的合理性与可行性。     

A new approach for numerical solution of integro-differential equations via Haar wavelets

A new method is proposed for numerical solution of Fredholm and Volterra integro-differential equations of second kind. The proposed method is based on Haar wavelets approximation. Special characteristics of Haar wavelets approximation has been used in the derivation of this method. The new method is the extension of the recent work [Aziz and Siraj-ul-Islam, New algorithms for numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets, J. Comput. Appl. Math. 239 (2013), pp. 333–345] from integral equations to integro-differential equations. The method is specifically derived for nonlinear problems. Two new algorithms are also proposed based on this new method, one each for numerical solution of Fredholm and Volterra integro-differential equations. The proposed algorithms are generic and are applicable to all types of both nonlinear Fredholm and Volterra integro-differential equations of second kind. The cost of the new algorithms is considerably reduced by using the Broyden's method instead of Newton's method for solution of system of nonlinear equations. Most of the numerical methods designed for solution of integro-differential equations rely on some other technique for numerical integration. The advantage of our method is that it does not use numerical integration. The integrand is approximated using Haar wavelets approximation and then exact integration is performed. The method is tested on number of problems and numerical results are compared with existing methods in the literature. The numerical results indicate that accuracy of the obtained solutions is reasonably high even when the number of collocation points is small.     

Partitioning and preconditioning of finite element matrices on the DAP

A method for solving linear finite element equations is proposed for highly parallel SIMD architectures with limited local memory. The method is based on a fine domain decomposition that can be conveniently mapped onto the processor array. Then the equations are structured using a form of one-way dissection and the equations solved by an iteration that combines conjugate gradient relaxation with coarse grid smoothing. Numerical experiments using the 64 × 64 DAP are presented.     

求解二维三温能量方程的半粗化代数多重网格法

§1.引言 二维三温辐射流体动力学方程组的求解是数值模拟的重要组成部分,而求解能量方程是一个十分重要的环节,而且在整个系统的计算中,能量方程求解所占的机时比重相当大(约80％以上)。因此,寻求一个收敛快、稳定性好的二维三温能量方程数值解法是一个值得探讨     

Estimating Components of Univariate Gaussian Mixtures Using Prony's Method

A new technique for estimating the component parameters of a mixture of univariate Gaussian distributions using the method of moments is presented. The method of moments basically involves equating the sample moments to the corresponding mixture moments expressed in terms of component parameters and solving these equations for the unknown parameters. These moment equations, however, are nonlinear in the unknown parameters, and heretofore, an analytic solution of these equations has been obtained only for two-component mixtures [2]. Numerical solutions also tend to be unreliable for more than two components, due to the large number of nonlinear equations and parameters to be solved for. In this correspondence, under the condition that the component distributions have equal variances or equal means, the nonlinear moment equations are transformed into a set of linear equations using Prony's method. The solution of these equations for the unknown parameters is analytically feasible and numerically reliable for mixtures with several components. Numerous examples using the proposed technique for two-, three-, and four-component mixtures are presented.     

并行PCG算法在电法勘探中的应用研究

采用有限元法进行电法勘探时,会产生大型稀疏线性方程组,如何提高方程组的求解效率成为物探研究的关键。针对传统直接法难以实现并行求解的缺点,提出了在Beowulf集群环境下,采用并行PCG算法求解物探系统线性方程组。在集群环境下,该算法具有机器间相互通讯少、时间复杂度低等优点,并且易于并行实现。实验结果表明,采用PCG算法获得了良好的并行效果。     

并行PCG算法在电法勘探中的应用研究

采用有限元法进行电法勘探时,会产生大型稀疏线性方程组,如何提高方程组的求解效率成为物探研究的关键。针对传统直接法难以实现并行求解的缺点,提出了在Beowulf集群环境下,采用并行PCG算法求解物探系统线性方程组。在集群环境下,该算法具有机器间相互通讯少、时间复杂度低等优点,并且易于并行实现。实验结果表明,采用PCG算法获得了良好的并行效果。     

并行PCG算法在电法勘探中的应用研究

采用有限元法进行电法勘探时，会产生大型稀疏线性方程组，如何提高方程组的求解效率成为物探研究的关键。针对传统直接法难以实现并行求解的缺点，提出了在Beowulf集群环境下，采用并行PCG算法求解物探系统线性方程组。在集群环境下，该算法具有机器间相互通讯少、时间复杂度低等优点，并且易于并行实现。实验结果表明，采用PCG算法获得了良好的并行效果。     

基于MATLAB的非线性方程组遗传解法

将非线性方程组的求解问题转化为用遗传算法求解目标函数的最小值问题,利用MATLAB的遗传算法与直接搜索工具箱（GADs）对目标函数求取最小值。计算结果表明,用该方法求得的非线性方程组近似解精度较高。     

Computation of Sharp Rigorous Componentwise Error Bounds for the Approximate Solutions of Systems of Linear Equations

This paper is concerned with the problem of verifying the accuracy of approximate solutions of systems of linear equations. Recently, fast algorithms for calculating guaranteed error bounds of computed solutions of systems of linear equations have been proposed using the rounding mode controlled verification method and the residual iterative verification method. In this paper, a new verification method for systems of linear equations is proposed. Using this verification method, componentwise verified error bounds of approximate solutions of systems of linear equations can be calculated. Numerical results are presented to illustrate that it is possible to get very sharp error bounds of computed solutions of systems of linear equations whose coefficient matrices are symmetric and positive definite.     

Solving Systems of Linear Fuzzy Equations by Parametric Functions

Buckley and Qu proposed a method to solve systems of linear fuzzy equations. Basically, in their method the solutions of all systems of linear crisp equations formed by the alpha-levels are calculated. We propose in this paper a new method for solving systems of linear fuzzy equations based on a practical algorithm using parametric functions in which the variables are given by the fuzzy coefficients of the system. We show that our algorithm is much more efficient than the method of Buckley and Qu.