Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem.

Adapted Metrics for a Modified Coulomb/Newton’s Potential

Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns.

ON AMODIFIED NEWTON'S METHOD AND CONVERGENCE

In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two steps compared with Newton’s method. A convergence theorem is established by using a weak condition a≤3-2(21/2) and a sharp error estimate is given about the iterative sequence.

Modified Efficient Families of Two and Three-Step Predictor-Corrector Iterative Methods for Solving Nonlinear Equations

In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting near the root. The main advantage of our methods is that they perform better and moreover, have the same efficiency indices as that of existing multipoint iterative methods. Furthermore, the convergence analysis of the new methods is discussed and several examples are given to illustrate their efficiency.

A Family of Fifth-order Iterative Methods for Solving Nonlinear Equations

In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order five. Numerical examples show that the new methods are comparable with the well known existing methods and give better results in many aspects.

Q-Theory: A Connection between Newton’s Law and Coulomb’s Law?

Assuming a Winterberg model for space where the vacuum consists of a very stiff two-component superfluid made up of positive and negative mass planckions, Q theory is the hypothesis, that Planck charge, qpl, was created at the same time as Planck mass. Moreover, the repulsive force that like-mass planckions experience is, in reality, due to the electrostatic force of repulsion between like charges. These forces also give rise to what appears to be a gravitational force of attraction between two like planckions, but this is an illusion. In reality, gravity is electrostatic in origin if our model is correct. We determine the spring constant associated with planckion masses, and find that, , where ζ(3) equals Apery’s constant, 1.202 …, and, n+(0)=n_(0), is the relaxed, i.e., , number density of the positive and negative mass planckions. In the present epoch, we estimate that, n+(0) equals, 7.848E54 m-3, and the relaxed distance of separation between nearest neighbor positive, or negative, planckion pairs is, l+(0)=l_(0)=5.032E-19 meters. These values were determined using box quantization for the positive and negative mass planckions, and considering transitions between energy states, much like as in the hydrogen atom. For the cosmos as a whole, given a net smeared macroscopic gravitational field of, , due to all the ordinary, and bound, matter contained within the observable universe, an average displacement from equilibrium for the planckion masses is a mere 7.566E-48 meters, within the vacuum made up of these particles. On the surface of the earth, where, g=9.81m/s2, the displacement amounts to, 7.824E-38 meters. All of these displacements are due to increased gravitational pressure within the vacuum, which in turn is caused by applied gravitational fields. The gravitational potential is also derived and directly related to gravitational pressure.

The Continuous Analogy of Newton’s Method for Solving a System of Linear Algebraic Equations

We propose a continuous analogy of Newton’s method with inner iteration for solving a system of linear algebraic equations. Implementation of inner iterations is carried out in two ways. The former is to fix the number of inner iterations in advance. The latter is to use the inexact Newton method for solution of the linear system of equations that arises at each stage of outer iterations. We give some new choices of iteration parameter and of forcing term, that ensure the convergence of iterations. The performance and efficiency of the proposed iteration is illustrated by numerical examples that represent a wide range of typical systems.

A New Modification of Newton Method with Cubic Convergence

Newton’s method is used to find the roots of a system of equations f (x) = 0. It is one of the most important procedures in numerical analysis, and its applicability extends to differential equations and integral equations. Analysis of the method shows a quadratic convergence under certain assumptions. For several years, researchers have improved the method by proposing modified Newton methods with salutary efforts. A modification of the Newton’s method was proposed by McDougall and Wotherspoon [1] with an order of convergence of 1+ √2. On a new type of methods with cubic convergence was proposed by H. H. H. Homeier [2]. In this article, we present a new modification of Newton method based on secant method. Analysis of convergence shows that the new method is cubically convergent. Our method requires an evaluation of the function and one of its derivatives.

New Fourth Order Iterative Methods Second Derivative Free

In a recent paper, Noor and Khan [M. Aslam Noor, & W. A. Khan, (2012) New Iterative Methods for Solving Nonlinear Equation by Using Homotopy Perturbation Method, Applied Mathematics and Computation, 219, 3565-3574], suggested a fourth-order method for solving nonlinear equations. Per iteration in this method requires two evaluations of the function and two of its first derivatives;therefore, the efficiency index is 1.41421 as Newton’s method. In this paper, we modified this method and obtained a family of iterative methods for appropriate and suitable choice of the parameter. It should be noted that per iteration for the new methods requires two evaluations of the function and one evaluation of its first derivatives, so its efficiency index equals to 1.5874. Analysis of convergence shows that the methods are fourth-order. Several numerical examples are given to illustrate the performance of the presented methods.

MODIFIED BERNOULLI ITERATION METHODS FOR QUADRATIC MATRIX EQUATION

We construct a modified Bernoulli iteration method for solving the quadratic matrix equation AX^2 ＋ BX ＋ C = 0, where A, B and C are square matrices. This method is motivated from the Gauss-Seidel iteration for solving linear systems and the ShermanMorrison-Woodbury formula for updating matrices. Under suitable conditions, we prove the local linear convergence of the new method. An algorithm is presented to find the solution of the quadratic matrix equation and some numerical results are given to show the feasibility and the effectiveness of the algorithm. In addition, we also describe and analyze the block version of the modified Bernoulli iteration method.

基于改进Kaiser窗快速S变换和LightGBM的电能质量扰动识别与分类新方法

针对S变换在电能质量扰动检测中存在计算量过大,时频分辨率低,电能质量扰动数据集常具备类别不平衡的问题,提出一种基于改进Kaiser窗快速S变换(modified Kaiser window fast S-transform,FMKST)和轻梯度提升机(light gradient boosting machine,LightGBM)的电能质量扰动识别与分类新方法。首先通过快速傅里叶变换得到采样信号频谱;然后利用迭代循环滤波区间定位算法确定扰动频率区间;再根据扰动频率区间所处频段确定窗宽调节因子并对相应区间进行变换;最后从采样信号的FMKST模时频矩阵中提取特征向量并构建改进LightGBM分类器进行分类。仿真与实验结果表明,提出的方法具有更高的识别准确率与更快的诊断速度,适用于海量电能质量扰动数据的快速识别与分类。

NURBS插补中的速度规划与参数计算

为满足数控机床高速度、高质量加工的需求,提出一种新的非均匀有理B样条曲线插补算法。该算法包括速度规划和参数计算两部分。速度规划部分采用五段S曲线加减速控制方法,能够保证高速运行过程中加速度的连续,使机床运行平稳,避免产生激烈的震颤;参数计算部分应用抛物线插值结合牛顿迭代的方法计算插补参数,将实时插补时产生的进给速度波动控制到理想水平,从而进一步减小机床震颤。仿真实验表明,该算法能够减小机床振动,实现高质量加工。

基于S变换谱阈值去噪的冲击特征提取方法

提纯旋转机械设备故障振动信号中的冲击特征,可以有效地实现相关故障的诊断。利用S变换适合于处理冲击特征信号的特点,提出基于S变换谱阈值去噪的冲击特征提取方法。先将信号进行S变换,得到其时频谱。考虑到此S变换谱为一复数矩阵,故而根据谱系数的模值大小进行阈值去噪。去噪过程中分别采用了基本的硬阈值函数和软阈值函数。对于最优阈值的估计,以所提出的改进风险函数为评价标准,利用步长迭代算法在零到系数最大模值的区间内获取。最后将去噪后的时频谱进行S逆变换,重构得到时域冲击特征。仿真信号与滚动轴承故障振动信号的处理结果表明,利用所获取的最优阈值,S变换谱阈值去噪方法能够从噪声混合信号中提取出冲击特征,从而实现相关故障的诊断。

基于NURBS插补算法的汽轮机叶片数控加工

为了提高汽轮机叶片的加工精度,文章通过分析汽轮机叶片的结构特点,采用一种NURBS曲线插补算法对其进行插补仿真。文章所采用算法由两部分组成:速度规划和参数计算。首先速度规划采用简化的五段S曲线加减速控制方法,保证了叶片在高速加工过程中加速度的连续,使机床运行平稳,然后利用牛顿迭代法来计算插补参数,得到更精确的插补参数,进一步提高了叶片的加工精度和加工速度。汽轮机叶片的插补仿真表明,该算法有高的稳定性和运算精度,并且使机床振动减小,速度波动小,保证了叶片的高质量加工。

NLS问题的正则化修正高斯-牛顿法

本文借助于正则化理论,通过添加稳定泛函μΩ(z)=μ2‖xk-xk-1‖2,结合修正高斯-牛顿法,构造了非线性最小二乘问题正则化修正高斯-牛顿法求解公式;解决了普通修正高斯-牛顿法在迭代过程中其Jacobian矩阵是秩亏或者严重病态导致的不能收敛的问题;给出了非线性秩亏自由网平差的正则化修正高斯-牛顿法步骤;最后以几个经典非线性最小二乘问题为例进行了数值实验,说明了本文所提方法的正确性和适用性。

应用SAS解非线性回归问题

.应用SAS/STAT估计非线性回归模型中的参数.首先,通过变量代换,把可以线性化的非线性回归模型化为线性回归模型,并用普通最小二乘法、主成分分析法和偏最小二乘法求模型中的参数和回归模型.其次,通过改良的高斯—牛顿迭代法来估计Logistic模型和Compertz模型中的参数.

具有可调参数的不带导数的修正Newton法

讨论了一种解非线性方程的具有可调参数的不带导数的修正Newton法 .文章根据动力系统的原理 ,以特殊割线的斜率及变参数代替导数值 ,推导出一种修正Newton法与Steffensen加速法相结合的迭代公式 ,并且在较弱条件下 ,证明了其与修正Newton法至少有相同的收敛速度 ,最后给出了数值结果 .该迭代法的优点是毋需调用导数值 ;可调节收敛速度 .

轴旋转法标定中的机器人运动学建模方法研究

轴旋转法标定是通过依次旋转机器人关节轴获取测量点,利用测量点拟合机器人轴线方程。基于轴线方程,利用两种方法建立机器人运动学方程,第一种方法首先求取机器人各轴理论坐标系相对于基坐标系的变换矩阵,然后基于理论轴线与实际轴线间的微小误差,求取各轴实际坐标系相对于基坐标系的变换矩阵,最后求取六变量相邻变换矩阵。第二种方法是直接利用新MDH法求取实际机器人的相邻变换矩阵,即对于空间交叉轴,求其公垂线确定轴坐标系,对于平行轴,通过交叉轴的公垂线交点向另一轴作垂线,确定另一轴坐标系的x轴方向。比较两种方法发现,第一种方法无法求解各轴的零位偏差,而第二种方法可以解耦求取各轴零位偏差与几何参数。利用牛顿迭代法求解两种模型的逆运动学方程,并用实验和仿真计算比较两种方法的标定效果,其轨迹精度达到−0.83~+0.52 mm。

简化Newton迭代的点估计和收敛域

设ｆ：Ｅ→Ｆ是Ｂａｎａｃｈ空间Ｅ的某个区域到同型空间Ｆ的Ｆｒｃｈｅｔ可微的算子，Ａ：Ｆ→Ｅ是一个相反的固定的线性算子．称迭代ｚｎ＋１＝ｚｎ－Ａｆ（ｚｎ）为简化Ｎｅｗｔｏｎ迭代，其中ｎ∈Ｎ０，Ａ＝Ｄｆ（ｚ０）－１．用Канторович的区域判据和Ｓｍａｌｅ的点估计判据研究广义简化Ｎｅｗｔｏｎ迭代的收敛性和收敛域的大小，并且包括当α（ｆ，ｚ）≤３－２２时广义简化Ｎｅｗｔｏｎ迭代收敛情况．

始末速度不为零的S型加减速时间规划算法研究

针对始末速度不为零的非对称S型加减速时间难以规划问题,把加速度曲线分为7个时间段,对关于加速度变化时间的方程组进行分析,化简为一元高次方程,并根据其变化的单调性构造其平方函数,使其转换为单一凸形函数,进而利用牛顿迭代求出其收敛值并根据效率最优原则和加速度、速度约束条件进行修正;对匀加速度时间的规划,直接根据其公式特点,转换为一元二次方程进行规划并根据效率最优原则和加速度、速度约束条件进行修正;对于匀速运动时间直接根据一元一次方程的解法进行规划。该算法解决了现有始末速度不为零的S型加减速时间规划过程复杂、繁琐问题,提供了一种简洁、高效的加减速时间规划算法。通过仿真与试验可知,本算法求解效率提高10.8%,插补效率提高1.32%,插补效果满足精度要求,同时证明了该算法简洁、高效、运行稳定、能够满足高速高精数控要求。