径向基插值BFGP算法的一种异步并行格式

本文研究了多变量散乱数据插值问题,利用径向基函数方法,得到了并行迭代格式及其收敛性,改进了BFGP算法.     

单调线性互补问题的一种内点算法

本文研究了单调线性互补问题的一种内点算法.利用牛顿方向和中心路径方向,获得了求解单调线性互补问题的一种内点算法,并证明该算法经过多项式次迭代之后收敛到原问题的一个最优解.数值实验表明此方法是有效的.     

基于蚁群优化的MPPT算法研究

为了提高光伏发电系统最大功率点跟踪效果,提出了一种蚁群优化算法,算法通过迭代法更新占空比来趋近光伏电池的最大功率点.利用MATLAB软件对光伏电池进行建模与仿真,仿真结果验证了算法的可行性,并说明了算法能够快速地跟踪最大功率点.     

基于代数等价变换下的凸二次规划不可行内点算法

基于代数等价变换和在KMM算法的框架基础上,在原始-对偶内点方法的牛顿方程里嵌入一种自调节功能.从而对凸二次规划提出了一种新的迭代方向的不可行内点算法,并证明了算法的全局收敛性.     

散乱数据带自然边界条件二元样条光顺及数值微分

考虑一种新的散乱数据带自然边界二元样条光顺问题.根据样条变分理论和Hilbert空间样条函数方法,构造出了显式的二元带自然边界光顺样条解,其表达式简单且系数可以由系数矩阵对称正定的线性方程组确定.证明了解的存在和唯一性,讨论了收敛性和误差估计.并由此得到一种新的基于散乱数据上的正则化二元数值微分的方法.最后,给出了一些数值例子对方法进行了验证.     

一个新的目标罚函数算法

提出了求解约束优化问题的一种新的目标罚函数算法,这种目标罚函数的形式借助于目标罚函数、障碍函数、外部罚函数三种思想构成,提出了一个算法,并证明了算法的收敛性.新算法的一个特点是可以任意选择开始点进行迭代,数值实验结果表明了算法对于不同的初始点的有效性.     

一种基于邻近点算法的变步长原始-对偶算法

本文考虑求解一种源于信号及图像处理问题的鞍点问题.基于邻近点算法的思想,我们对原始-对偶算法进行改进,构造一种对称正定且可变的邻近项矩阵,得到一种新的原始-对偶算法.新算法可以看成一种邻近点算法,因此它的收敛性易于分析,且无需较强的假设条件.初步实验结果表明,当新算法被应用于求解图像去模糊问题时,和其他几种主流的高效算法相比,新算法能得到较高质量的结果,且计算时间也是有竞争力的.     

非线性约束优化问题的混合粒子群算法

把处理约束条件的一个外点方法和改进的粒子群优化算法相结合,提出了一种求解非线性约束优化问题的混合粒子群优化算法.该方法兼顾了粒子群优化和外点法的优点,对算法迭代过程中出现不可行粒子,利用外点法处理后产生可行粒子.数值实验表明了提出的新算法具有有效性、通用性和稳健性.     

多变点检测问题的Shape-based BS算法

BS算法是时间序列多变点检测中最经典的算法之一,但是基于全局CUSUM统计量的识别过程会带来过多误判和较高的时间复杂度.BS算法是一种离线的序贯方法,因此没有充分利用数据的时序信息;另一方面,BS算法识别变点的原则是CUSUM统计量最大化,也没有考虑统计量构成序列的形态特性.鉴于此,提出一种基于局部形态识别的BS改进算法,命名为Shape-based BS算法.基于局部形态识别统计量,不仅大大降低计算复杂度,且降低了因变点间的互相干扰而带来的误判率,进而提升变点识别的稳健性.最后,将此算法应用到了电力系统的"场景压缩"问题上,具有满意的实用效果.     

一种求解非线性互补问题的filter内点算法

利用Armijio条件和信赖域方法,构造新的价值函数.首次将内点算法与filter技术结合起来,提出一种求解非线性互补问题的新算法,即filter内点算法.在主算法中使用Armijio型线搜索求取步长,在修复算法中使用信赖域方法进行适当控制以保证算法的收敛性.文章还讨论了算法的全局收敛性.最后用数值实验表明了该方法是有效的.     

条件正定矩阵及其在多元插值计算中的应用

这里A一般不是正定的,按后面定义只是“条件正定”的,特别,A的对角线元素往往是零.这给方程组的求解带来了困难.我们的目的是如何利用“条件正定”的特点建立有效的算法,减少计算量和机器时间.为此,先讨论“条件正定”矩阵及与之相关的“条件正定”函数的某些性质,以便于判定A的条件正定性.然后利用这个性质构造有效算法.最后的平板样条数值结果表明,应用“条件正定”作工具建立的算法,比通常算法求解(1)的效率提高四倍以上.     

基于层次T网格的分片孔斯曲面重构

本文提出一种基于任意层次T网格的多项式(PHT)样条空间$S(3,3,1,1,T)$的一个新的曲面重构算法.该算法由分片插值于层次T网格上每个小矩形单元对应4个顶点的16个参数的孔斯曲面形式给出.对于一个给定的T网格和相应基点处的几何信息(函数值,两个一阶偏导数和混合导数值),可得到与$S(3,3,1,1,T)$的PHT样条曲面相同的结果,且曲面表达形式更简单,同时,在离散数据点的曲面拟合中,我们给出了自适应的曲面加细算法.数值算例显示,该自适应算法能够有效的拟合离散数据点.     

Scattered and track data interpolation using an efficient strip searching procedure

A new local algorithm for bivariate interpolation of large sets of scattered and track data is presented. The method, which changes partially depending on the kind of data, is based on the partition of the interpolation domain in a suitable number of parallel strips, and, starting from these, on the construction for any data point of a square neighbourhood containing a convenient number of data points. Then, the well-known modified Shepard’s formula for surface interpolation is applied with some effective improvements. The proposed algorithm is very fast, owing to the optimal nearest neighbour searching, and achieves good accuracy. Computational cost and storage requirements are analyzed. Moreover, the efficiency and reliability of the algorithm are shown by several numerical tests, also performed by Renka’s algorithm for a comparison.     

On the reconstruction of Dirichlet-to-Neumann map in inverse scattering problems with stability estimates

Consider the determination of Dirichlet-to-Neumann (D-to-N) map from the far-field pattern in inverse scattering problems, which is the key step in some recently developed inversion schemes such as probe method. Essentially, this problem is related to the reconstruction of the scattered wave from its far-field data. We firstly prove the well-known uniqueness result of the D-to-N map from the far-field pattern using a new scheme based on the mixed reciprocity principle. The advantage of this new proof scheme is that it provides an efficient algorithm for computing the D-to-N map, avoiding the numerical differentiation for the scattered wave. Then combining with the classical potential theory, a simple and feasible regularizing reconstruction scheme for the D-to-N map is proposed. Finally the stability estimate for the reconstruction with noisy input data is rigorously analyzed.     

Low-Cost Numerical Method for Solving a Coefficient Inverse Problem for the Wave Equation in Three-Dimensional Space

For the acoustic-sensing problem of determining the characteristics of a local inhomogeneity scattering a wave field in three-dimensional space, a numerical algorithm is proposed and justified that is efficient in terms of computational resources and CPU time. The algorithm is based on the fast Fourier transform, which is used under certain a priori assumptions on the character of the inhomogeneity and the observation domain of the scattered field. Typical numerical results obtained by solving this inverse problem with simulated data on a personal computer are presented, which demonstrate the capabilities of the algorithm.     

Fast and accurate interpolation of large scattered data sets on the sphere

In this paper a new efficient algorithm for spherical interpolation of large scattered data sets is presented. The solution method is local and involves a modified spherical Shepard’s interpolant, which uses zonal basis functions as local approximants. The associated algorithm is implemented and optimized by applying a nearest neighbour searching procedure on the sphere. Specifically, this technique is mainly based on the partition of the sphere in a suitable number of spherical zones, the construction of spherical caps as local neighbourhoods for each node, and finally the employment of a spherical zone searching procedure. Computational cost and storage requirements of the spherical algorithm are analyzed. Moreover, several numerical results show the good accuracy of the method and the high efficiency of the proposed algorithm.     

Spherical interpolation using the partition of unity method: An efficient and flexible algorithm

An efficient and flexible algorithm for the spherical interpolation of large scattered data sets is proposed. It is based on a partition of unity method on the sphere and uses spherical radial basis functions as local approximants. This technique exploits a suitable partition of the sphere into a number of spherical zones, the construction of a certain number of cells such that the sphere is contained in the union of the cells, with some mild overlap among the cells, and finally the employment of an optimized spherical zone searching procedure. Some numerical experiments show the good accuracy of the spherical partition of unity method and the high efficiency of the algorithm.     

圆形区域分散布局问题研究

针对圆形区域分散布局问题, 文中给出了一个带约束的非线性规划模型. 当布局点数量较少时, 通过将模型转化为无约束优化问题, 利用梯度方法进行求解; 对于布局点数量较多的情况, 提出了一个界为1/2的多项式时间的近似算法, 并进行了相应的算例分析, 进一步来验证算法解的合理性. 研究的结论及方法一定程度上丰富和完善了圆形区域的分散布局理论.     

Fast surface reconstruction and hole filling using positive definite radial basis functions

Surface reconstruction from large unorganized data sets is very challenging, especially if the data present undesired holes. This is usually the case when the data come from laser scanner 3D acquisitions or if they represent damaged objects to be restored. An attractive field of research focuses on situations in which these holes are too geometrically and topologically complex to fill using triangulation algorithms. In this work a local approach to surface reconstruction from point-clouds based on positive definite Radial Basis Functions (RBF) is presented that progressively fills the holes by expanding the neighbouring information. The method is based on the algorithm introduced in [7] which has been successfully tested for the smooth multivariate interpolation of large scattered data sets. The local nature of the algorithm allows for real time handling of large amounts of data, since the computation is limited to suitable small areas, thus avoiding the critical efficiency problem involved in RBF multivariate interpolation. Several tests on simulated and real data sets demonstrate the efficiency and the quality of the reconstructions obtained using the proposed algorithm. AMS subject classification 65D17, 65D05, 65Y20     

Monotone interpolation of scattered data in R s

We present a method to interpolate scattered monotone data in R ^s using a variational approach. We present both theoretical and practical properties and give a dual algorithm allowing us to compute the resulting function whens=2. The method is specially suited for scattered data but comparison with existing methods for data on grids shows that it is a valid approach even in that case.Communicated by Wolfgang Dahmen.