Successive overrelaxation method with projection for finite element solutions of nonlinear radiation cooling problems

In this paper, we consider the successive overrelaxation method with projection for obtaining the finite element solutions under the nonlinear radiation boundary conditions. In particular we establish the convergence of the successive overrelaxation method with projection. Some numerical results are also given to illustrate the usefulness.     

The determination of optimum accelerating factors for successive overrelaxation on an equidistant and non-equidistant rectangular net

A modification to the successive overrelaxation iterative procedure for solving elliptic partial differential equations is presented. The modified method is based on an extension of Brazier's nodal overrelaxation method in one dimension, characterised by the use of a different overrelaxation factor for each point in the net. The extension to several dimensions make use of the separability of the variables for the error distribution. Thus the optimum one dimensional results are directly used in the several dimensional problem.The present method has been examined in one and two dimensions, for equidistant and non-equidistant nets. The computational time required to obtain a given accuracy for a solution was found for all two dimensional cases to be half (or less) of that required by conventional methods.     

Alternating splitting waveform relaxation method and its successive overrelaxation acceleration

For the large sparse implicit linear initial value problem, we present a block successive overrelaxation scheme for the alternating direction implicit waveform relaxation method to further accelerate its convergence speed, and discuss the convergence property of the resulting iteration method in detail. Numerical implementations about several non-Hermitian implicit linear initial value problems show that the alternating direction implicit waveform relaxation method is very effective, and the block successive overrelaxation technique really accelerates its convergence speed.     

Convergence of the interval and point TOR method

In this paper, we present the interval version of the two parameter overrelaxation iterative (TOR) method and we obtain some convergence conditions when the matrix A of the linear system Ax?=?b belongs to some classes of matrice. Similar conditions were obtained for the point TOR method.

Some results for the accelerated overrelaxation interval and point iterative (AOR) method were also obtained, which coincides with those given by Martins in Ref. [7].     

The eigenvalue problem (A − λB)x = 0 for symmetric matrices of high order

Vibrational problems of complex structures treated by the method of finite elements lead to the general eigenvalue problem $\text{(A ? λB)x = 0}$, where $\text{A}$ and $\text{B}$ are symmetric and sparse matrices of high order. The smallest eigenvalues and corresponding eigenvectors of interest are usually computed by a variant of the inverse vector iteration. Instead of this, the smallest eigenvalue can be computed as the minimum of the corresponding Rayleigh quotient for instance by the method of the coordinate relaxation of Faddejew/Faddejewa. The slow convergence of this simple algorithm can however be sped up considerably in analogy to the successive overrelaxation method by a systematic overrelaxation. Numerical experiments indicate indeed a rate of convergence of this coordinate overrelaxation as a function of the relaxation parameter which is comparable to that of the usual seccessive overrelaxation for linear equations. In comparison with known procedures for the solution of the general eigenvalue problem there result some important computational advantages with regard to the amount of work. Finally, the higher eigenvalues can be computed successively by minimizing the Rayleigh quotient of a modified eigenvalue problem based on a deflation process.     

SORR回归算法在胆固醇测定中的应用

借鉴分类问题的算法,推广到回归问题中去,针对用于分类问题的SOR(successive overrelaxation for support vector)支持向量机算法,提出SORR(successive overrelaxation for support vector regression)支持向量回归算法,并应用于医学上三类血浆脂蛋白(VLDL、LDL、HDL)测定样本中胆固醇的含量。数值实验表明:SORR算法有效,与标准的支持向量回归SVR算法相比,保持了相同的回归精度,提高了学习速度,为临床上测定胆固醇含量提供新的有效方法。     

Note To The Mixed-Type Splitting Iterative Method For The Positive Real Linear System

In [5] a new iterative method is given for the linear system of equations Au=b , where A is large, sparse and nonsymmetrical and A^{\rm T}+A is symmetric and positive definite (SPD) or equivalently A is positive real. The new iterative method is based on a mixed-type splitting of the matrix A and is called the mixed-type splitting iterative method. The iterative method contains an auxiliary matrix D_1 that is restricted to be symmetric. In this note, the auxiliary matrix is allowed to be more general and it is shown that by proper choice of D 1 , the new iterative method is still convergent. It is also shown that by special choice of D_{1} , the new iterative method becomes the well-known (point) accelerated overrelaxation (AOR) [1] method. Hence, it is shown that the (point) AOR method applied to the positive real system is convergent under the proper choice of the overrelaxation parameters y and .     

A modified symmetric successive overrelaxation method for augmented systems

In this paper, we establish a modified symmetric successive overrelaxation (MSSOR) method, to solve augmented systems of linear equations, which uses two relaxation parameters. This method is an extension of the symmetric SOR (SSOR) iterative method. The convergence of the MSSOR method for augmented systems is studied. Numerical examples show that the new method is an efficient method.     

具有超松弛因子的OSEM重建算法

创建了一种比 OSEM法更快收敛的、更灵活地适应临床要求的医学图象重建迭代算法 .通过引入超松弛因子 z改进现有的 OSEM图象迭代重建算法 ,在 z=1时 ,回复为通常的 OSEM,在 z>1时 ,合并引入非负约束和总计数归一化约束条件 ,保证迭代快速收敛 .使用计算机模拟数据和 SPECT心肌灌注投影数据对该算法进行验证 ,并同其他图象重建算法的结果进行了比较 ,该算法运算速度比同阶数的 OSEM快 1倍以上 ,且比同样迭代次数的更高阶数的 OSEM运算速度还要快 .该算法具有收敛速度快 ,使用灵活等优点 .     

拟线性对称超松弛形两步递推辨识算法

本文提出一种线性系统拟线性对称超松弛两步递推辨识新算法，并对其收敛性应用常微分方程的方法进行了分析。仿真结果表明算法和本文的收敛定理是一致的。     

连续超松弛支持向量机回归算法应用研究

支持向量回归问题的研究,对函数拟合(回归逼近)具有重要的理论和应用意义.借鉴分类问题的有效算法,将其推广到回归问题中来,针对用于分类问题的SOR支持向量机有效算法,提出了SORR支持向量回归算法.在若干不同维数的数据集上,对SORR算法、ASVR算法和LibSVM算法进行数值试验,并进行比较分析.数值实验结果表明,SORR算法是有效的,与当前流行的支持向量机回归算法相比,在回归精度和学习速度上都有一定的优势.     

The variational inequality formulation of a unidirectional gravity-driven free-boundary flow

We study a free-boundary problem arising from a unidirectional gravity-driven steady flow. Under certain geometrical assumptions, the free-boundary problem is equivalent to a complementarity problem, which, in turn, is shown to be equivalent to a variational inequality. Numerical results using a point successive overrelaxation method with projection are presented for specific geometries.     

广义修正HSS迭代法的超松弛加逮

通过推广修正埃尔米特和反埃尔米特（MHSS）迭代法,我们进一步得到了求解大型稀疏非埃尔米特正定线性方程组的广义MHSS（GMHSS）迭代法．基于不动点方程,我们还将超松弛（SOR）技术运用到了GMHSS迭代法,得到了关于GMHSS迭代法的SOR加速,并分析了它的收敛性．数值算例表明,SOR技术能够大大提高加速GMHSS迭代法的收敛效率．     

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.     

Analyse numerique du champ magnetique d'un alternateur par elements finis et sur-relaxation ponctuelle non lineaire

The purpose of this paper is to study a method of solution of the two-dimensional non-linear partial differential equation describing the magnetic state in the cross-section of an alternator.The method used is based on the combination of finite element technique with various non-linear successive point overrelaxation algorithms. We obtain a method which is very robust and efficient and gives the possibility of solving easily, even on middle-size computers, the previous problem on complicated geometries. Convergence proofs for the finite element approximation and iterative algorithms are given.     

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.     

Accelerated convergence of the numerical simulation of incompressible flow in general curvilinear co-ordinates by discretizations on overset grids

The convergence rate of a methodology for solving incompressible flow in general curvilinear co-ordinates is analyzed. Overset grids (double-staggered grids type), each defined by the same boundaries as the physical domain are used for discretization. Both grids are Marker and Cell (MAC) quadrilateral meshes with scalar variables (pressure, temperature, etc.) arranged at the center and the Cartesian velocity components at the middle of the sides of the mesh. The problem was checked against benchmark solutions of natural convection in a squeezed cavity, heat transfer in concentric and eccentric horizontal cylindrical annuli and hot cylinder in a duct. Convergence properties of Poisson’s pressure equations which arise from application of the SIMPLE-like procedure are analyzed by several methods: successive overrelaxation, symmetric successive overrelaxation, modified incomplete factorization, and conjugate gradient. A genetic algorithm was developed to solve problems of numerical optimization of calculation time, in a space of iteration numbers and relaxation factors. The application provides a means of making an unbiased comparison between the double-staggered grids method and the standard interpolation method. Furthermore, the convergence rate was demonstrated with the well-known calculation of natural convection heat transfer in concentric horizontal cylindrical annuli. Calculation times when double staggered grids were used were 6–10 times shorter than those achieved by interpolation.     

Chebyshev polynomial acceleration for block SOR methods for solving the rank-deficient least-squares problem

In this article, we give the acceleration of the block successive overrelaxation (SOR) method for solving the rank-deficient least-squares problem. Santos and Silva proposed the two-block SOR method and the three-block SOR method. Here, we consider the acceleration of the two-block SOR method and the three-block SOR method using the Chebyshev polynomial and derive what we term the C-2-block SOR method and the C-3-block SOR method. The advantage of our methods is that we can get good results with very small iteration number. The comparison between the C-2-block method and the C-3-block method is presented. Finally, numerical examples are given.     

Global convergence of nonlinear successive overrelaxation via linear theory

The global convergence of nonlinear successive overrelaxation is established by utilising estimates from linear SOR theory.     

An iterative method for computing multivariate C piecewise polynomial interpolants

This paper describes a successive overrelaxation (SOR) method for computing a multivariate C¹ piecewise polynomial interpolant. Given a collection of points in R^m together with a triangulation of those points, the scheme described requires only the values of the function to be interpolated at the given points. The result is a C¹ interpolant whose restriction to each of the triangles in the triangulation is a polynomial of degree n.