GSOR Method for the Equality Constrained Least Squares Problems and the Generalized Least Squares Problems

In a recent paper [4], Li et al . gave a generalized successive overrelaxation (GSOR) method for the least squares problems. In this paper, we show that the GSOR method can be applied to the equality constrained least squares (LSE) problems and the generalized least squares (GLS) problems.     

Robust fuzzy regression analysis

In this paper we propose a robust fuzzy linear regression model based on the Least Median Squares-Weighted Least Squares (LMS-WLS) estimation procedure. The proposed model is general enough to deal with data contaminated by outliers due to measurement errors or extracted from highly skewed or heavy tailed distributions. We also define suitable goodness of fit indices useful to evaluate the performances of the proposed model. The effectiveness of our model in reducing the outliers influence is shown by using applicative examples, based both on simulated and real data, and by a simulation study.     

基于改进支持向量机的快速稳健代理模型研究

最小二乘支持向量机代理模型具有较好的泛化能力和强大的非线性处理能力,但其对实际工程中不可避免的异常样本十分敏感,而传统的加权最小二乘支持向量机易产生过度拟合并且未考虑到回归误差分布特性,针对这一问题提出正态分布概率密度函数加权方法,并且采用回归误差的中值作为计算权值的衡量标准,增强了加权算法的稳健性;提出了迭代加权最小二乘支持向量机快速递推算法,利用矩阵关系进行迭代递推计算,减少了计算量,节约了建模时间。通过数值实例验证了该方法的可行性、有效性。     

基于支持向量回归的单步多分类算法

分析了利用支持向量回归求解多分类问题的思想,提出了一种基于局部密度比权重设置模型的加权最小二乘支持向量回归模型来单步求解多分类问题：该方法先分别对类样本中每类样本利用局部密度比权重设置模型求出每个样本的权重隶属因子,然后运用加权最小二乘支持向量回归算法对所有样本进行训练,获得回归分类器。为验证算法的有效性,对UCI三个标准数据集以及一个随机生成的数据集进行实验,对比了多种单步求解多分类问题的算法,结果表明,提出的模型分类精度高,具有良好的鲁棒性和泛化性能。     

Approximate polynomial preconditionings applied to biharmonic equations

Applying a finite difference approximation to a biharmonic equation results in a very ill conditioned system of equations. This paper examines the conjugate gradient method used with polynomial preconditioning techniques for solving such linear systems. A new approach using an approximate polynomial preconditioner is described. The preconditioner is constructed from a series approximation based on the Laplacian finite difference matrix. A particularly attractive feature of this approach is that the Laplacian matrix consists of far fewer non-zero entries than the biharmonic finite difference matrix. Moreover, analytical estimates and computational results show that this preconditioner is more effective (in terms of the rate of convergence and the computational work required per iteration) than the polynomial preconditioner based on the original biharmonic matrix operator. The conjugate gradient algorithm and the preconditioning step can be efficiently implemented on a vector super-computer such as the CDC CYBER 205.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada Grant U0375; and in part by NASA (funded under the Space Act Agreement C99066G) while the author was visiting ICOMP, NASA Lewis Research Center.The work of this author was supported by an Izaak Walton Killam Memorial Scholarship.     

非线性迭代PLS信息模式识别算法

对偏最小二乘(PLS)回归的基本方法进行了分析研究,提出了基于非线性迭代偏最小二乘(NIPLS)的信息模式识别算法。该算法实现了模式识别中特征提取与分类器设计的有机结合。NIPLS较Fisher判别分析、Bayes判别分析等经典的模式识别算法,具有更强的信息识别能力,且对数据本身的分布要求不高,尤其对于多重共线性资料或解释变量多而样本数量少时更为有效。将该算法应用于土地质量的分类识别,结果表明,该文所建立的算法是有效的、可靠的。     

An algebraic method for Schrödinger equations in quaternionic quantum mechanics

In the study of theory and numerical computations of quaternionic quantum mechanics and quantum chemistry, one of the most important tasks is to solve the Schrödinger equation with A an anti-self-adjoint real quaternion matrix, and |f〉 an eigenstate to A. The quaternionic Schrödinger equation plays an important role in quaternionic quantum mechanics, and it is known that the study of the quaternionic Schrödinger equation is reduced to the study of quaternionic eigen-equation Aα=αλ with A an anti-self-adjoint real quaternion matrix (time-independent). This paper, by means of complex representation of quaternion matrices, introduces concepts of norms of quaternion matrices, studies the problems of quaternionic Least Squares eigenproblem, and give a practical algebraic technique of computing approximate eigenvalues and eigenvectors of a quaternion matrix in quaternionic quantum mechanics.     

Block iterative methods for the numerical solution of three dimensional mildly non-linear biharmonic problems of first kind

In this article, we discuss two sets of new finite difference methods of order two and four using 19 and 27 grid points, respectively over a cubic domain for solving the three dimensional nonlinear elliptic biharmonic problems of first kind. For both the cases we use block iterative methods and a single computational cell. The numerical solution of (?u/?n) are obtained as by-product of the methods and we do not require fictitious points in order to approximate the boundary conditions. The resulting matrix system is solved by the block iterative method using a tri-diagonal solver. In numerical experiments the proposed methods are compared with the exact solutions both in singular and non-singular cases.     

Application of the Galerkin and Least-Squares Finite Element Methods in the solution of 3D Poisson and Helmholtz equations

This paper presents the numerical solution, by the Galerkin and Least Squares Finite Element Methods, of the three-dimensional Poisson and Helmholtz equations, representing heat diffusion in solids. For the two applications proposed, the analytical solutions found in the literature review were used to compare with the numerical solutions. The analysis of results was made from the L₂ norm (average error throughout the domain) and L_∞ norm (maximum error in the entire domain). The results of the two applications (Poisson and Helmholtz equations) are presented and discussed for testing of the efficiency of the methods.     

空间三角网格曲面的补洞方法

由三维扫描仪对文物表面进行扫描得到网格数据后,先提取出破洞的边界,利用破洞边界三角形的法矢信息将破洞边界上的点投影到一个平面上,形成一个二维多边形;然后基于该二维多边形各内角及各边长度在多边形内插入新的离散点,再将多边形内离散点三角网格化;最后用移动最小二乘近似法将破洞附近的点拟和成曲面,以此求出插入点的高度值,这样就得到了在三维空间中的网格数据。     

LDLT分块求解计算方法在有限元分析中的编程实现

针对有限元计算时遇到的大型线性方程组求解问题,提出一种解决方法,即对方程组的系数矩阵采用三角分解法,并用一维变带宽存贮,同时与分块法相结合,实现内存与外存数据的交换。这种方法节省内存,提高计算效率,且解决了内存资源不足的问题。实例表明这个算法是很有效的。     

有限元法在并行产品设计中的应用

文章研究了有限元法在并行产品设计中的应用,提出了典型产品的并行设计过程与方法,结合典型产品设计,研究了汽车车身并行虚拟样机方法。     

基于应用层负载均衡策略的分析与研究

介绍了Round Robin（RR）,Weighted Round Robin（WRR）,Least Connection（LC）和Weighted Least Connection（WLC）四种负载均衡算法,对这四种算法进行性能仿真。根据模拟得到的相关数据绘制各个算法的负载均衡度性能曲线,并对每个算法进行了性能分析。在此基础上设置三种不同的模拟模型,对四种算法进行更深入的测试和性能比较。     

PLS-LSSVM模型在锌净化中的应用

在锌净化除钴过程中,生产数据存在噪声且变量间具有多重相关性,从而难以准确预测钴离子浓度。为此,采用偏最小二乘方法去除数据中的噪声,降低各参数间的多重相关性。通过为不同时期的样本数据赋予不同的权值,提高了最小二乘支持向量机(LSSVM)模型预测的准确性。利用改进的粒子群优化算法优化选择LSSVM模型的惩罚因子和核函数参数,以避免人为选择参数的盲目性。仿真结果表明,PLS- LSSVM模型的预测精度高于偏最小二乘回归和LSSVM。     

Finite time blow-up for a class of parabolic or pseudo-parabolic equations

In this paper, we study the initial boundary value problem for a class of parabolic or pseudo-parabolic equations:

$u_t?a\Delta u_t?\Delta u+bu=k\left(t\right)|u{|}^{p?2}u,(x,t)\in \Omega \times (0,T),$

where $a\ge 0$, $b>?{?}_1$ with ${?}_1$ being the principal eigenvalue for $?\Delta$ on $H_0^1\left(\Omega \right)$ and $k\left(t\right)>0$. By using the potential well method, Levine’s concavity method and some differential inequality techniques, we obtain the finite time blow-up results provided that the initial energy satisfies three conditions: (i) $J(u_0;0)<0$; (ii) $J(u_0;0)\le d\left(\infty \right)$, where $d\left(\infty \right)$ is a nonnegative constant; (iii) $0<J(u_0;0)\le C\rho \left(0\right)$, where $\rho \left(0\right)$ involves the $L^2$-norm or $H_0^1$-norm of the initial data. We also establish the lower and upper bounds for the blow-up time. In particular, we obtain the existence of certain solutions blowing up in finite time with initial data at the Nehari manifold or at arbitrary energy level.     

Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation

In this paper, we first split the biharmonic equation Δ² u=f with nonhomogeneous essential boundary conditions into a system of two second order equations by introducing an auxiliary variable v=Δu and then apply an hp-mixed discontinuous Galerkin method to the resulting system. The unknown approximation v _h of v can easily be eliminated to reduce the discrete problem to a Schur complement system in u _h , which is an approximation of u. A direct approximation v _h of v can be obtained from the approximation u _h of u. Using piecewise polynomials of degree p≥3, a priori error estimates of u−u _h in the broken H ¹ norm as well as in L ² norm which are optimal in h and suboptimal in p are derived. Moreover, a priori error bound for v−v _h in L ² norm which is suboptimal in h and p is also discussed. When p=2, the preset method also converges, but with suboptimal convergence rate. Finally, numerical experiments are presented to illustrate the theoretical results. Supported by DST-DAAD (PPP-05) project.     

一种使用机器学习方法的数字水印算法

针对目前数字水印算法存在的不足,本文将离散小波变换和奇异值分解相结合,提出了一种基于机器学习的图像数字水印算法.首先将载体图像进行一级小波变换,提取其低频子带图像对其进行4×4分块处理,然后对每一分块进行奇异值分解后嵌入水印,并提取特征向量用于最小二乘支持向量机的训练,训练好的最小二乘支持向量机用于自适应最大水印嵌入强...     

Preconditioned Conjugate Gradient Method and Generalized Successive Overrelaxation Method for the Least Squares Problems

In a recent paper [4], Li et al . gave a generalized successive overrelaxation (GSOR) method for the least squares problems. In this paper, the connection between the GSOR method and the preconditioned conjugate gradient (PCG) method for the normal equations is investigated. It is shown that the PCG method is at least as fast as the GSOR method. Numerical examples demonstrates that the PCG method is much faster than the GSOR method.     

The weighted continuous galerkin scheme for ordinary differential equations

We introduce the Weighted Continuous Galerkin Scheme for initial value ordinary differential equations. This is an extension of the Continuous Galerkin Scheme, having an extra parameter for the purpose of error reduction. We prove convergence in the L ₂ norm in the time variable in a new way, similar to (elliptic) finite element techniques. Using the optimal L ₂ estimates, we then prove max norm convergence. Numerical evidence for the effectiveness of the proposed scheme is presented.     

New analytical method for solving Burgers' and nonlinear heat transfer equations and comparison with HAM

In this study, we present a numerical comparison between the differential transform method (DTM) and the homotopy analysis method (HAM) for solving Burgers' and nonlinear heat transfer problems. The first differential equation is the Burgers' equation serves as a useful model for many interesting problems in applied mathematics. The second one is the modeling equation of a straight fin with a temperature dependent thermal conductivity. In order to show the effectiveness of the DTM, the results obtained from the DTM is compared with available solutions obtained using the HAM [M.M. Rashidi, G. Domairry, S. Dinarvand, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 708-717; G. Domairry, M. Fazeli, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 489-499] and whit exact solutions. The method can easily be applied to many linear and nonlinear problems. It illustrates the validity and the great potential of the differential transform method in solving nonlinear partial differential equations. The obtained results reveal that the technique introduced here is very effective and convenient for solving nonlinear partial differential equations and nonlinear ordinary differential equations that we are found to be in good agreement with the exact solutions.