改进的变分迭代法在Klein-Gordon方程中的应用

讨论了如何利用改进的变分迭代法应用于Klein-Gordon方程,通过其简便的计算可以得到方程的解,与Adomian分裂法对比可知改进的变分迭代法求收敛解的速度比后者要快速、简单.

矩阵方程A^TXB+B^TX^TA=C的一般解及其最佳逼近解

用正交投影迭代法讨论了矩阵方程A^TXB+B^TX^TA=C的一般解及相应的最佳逼近解.首先利用矩阵的相关理论,给出了求矩阵方程的正交投影迭代解法,证明了算法的收敛性,并得出了收敛速率估计式;其次对该算法稍加修改,得到相应的最佳逼近.本文中,要求A,B实正规矩阵,且满足A^TB=BA^T,C是实矩阵.

广义Lyapunov方程A^TX+X^TA=C的一般解及其最佳逼近解

本文讨论矩阵方程ATX+XTA=C的一般解及其最佳逼近解的正交投影迭代解法.首先,利用矩阵的结构特点及相关性质,并借助矩阵空间的相关理论,给出求该矩阵方程一般解正交投影迭代算法;其次,根据奇异值分解、F-范数正交变换不变性证明算法的收敛性并推导出算法的收敛速率估计式,当方程相容时,该算法收敛于问题的极小范数解,且对该算法稍加修改,就可得到相应最佳逼近解;最后,用数值实例验证算法的有效性.

多曲线回归方法及计算机应用

利用方程迭代法， 研究并开发了实测资料非线性多族对应关系的多曲线计算机回归分析程序； 对宁夏青铜峡灌区实测水量资料进行了回归计算， 所得成果与手工整编成果吻合很好， 为灌区水量资料整编工作全面电算化奠定了基础。

机器人标定算法及在打磨机器人中的应用

首先介绍了机器人位姿匹配的基本原理,以及两种通用的机器人几何参数标定的优化算法:非线性优化方法和递归线性方程法,并分别利用这两种优化算法对打磨机器人的几何参数进行了标定.在此基础上,通过分析影响打磨机器人位置误差的因素,从参数集中剔除对位置误差影响不敏感和无法区分其影响效果的因素,再采用前述优化算法对机器人几何参数进行标定.仿真结果表明此标定效果和前者相比无显著差异,在一定情况下甚至优于前者.因此在标定过程中,可以采用把冗余参数去除来对机器人进行精确标定.

Multi-scale seismic full waveform inversion in the frequency-domain with a multi-grid method

Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.

Improvement of CORDIC Algorithm

Aim To discuss the basic CORDIC algorithm that can be applied to digital signal processing and its applying condition called convergence range.Methods In addition to the original basic equation, another group iterative equation was used to evaluate the correspondent values of input data that did not lie within the convergence range. Results and Conclusion The improved CORDIC algorithm removes the limits of the range of convergence and can adapt itself to the variations of input values. The correctness of improved CORDIC algorithms has been proved by calculating examples.

Contributions to Hom-Schunck optical flow equations-part I： Stability and rate of convergence of classical algorithm

Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iteration into a continuous flow. The stability condition depends explicitly on smoothness of the image sequence, size of image domain, value of the regularization parameter, and finally discretization step. Specifically, as the discretization step approaches to zero, stability holds unconditionally. The analysis also clarifies relations among the iterative algorithm, the original variation formulation and the PDE system. The proper regularity of solution and natural images is briefly surveyed and discussed. Experimental results validate the theoretical claims both on convergence and exponential stability.

Inverse kinematics of a heavy duty manipulator with 6-DOF based on dual quaternion

An iterative method is introduced successfully to solve the inverse kinematics of a 6-DOF manipulator of a tunnel drilling rig based on dual quaternion, which is difficult to get the solution by Denavit-Hartenberg(D-H) based methods. By the intuitive expression of dual quaternion to the orientation of rigid body, the coordinate frames assigned to each joint are established all in the same orientation, which does not need to use the D-H procedure. The compact and simple form of kinematic equations, consisting of position equations and orientation equations, is also the consequence of dual quaternion calculations. The iterative process is basically of two steps which are related to solving the position equations and orientation equations correspondingly. First, assume an initial value of the iterative variable; then, the position equations can be solved because of the reduced number of unknown variables in the position equations and the orientation equations can be solved by applying the solution from the position equations, which obtains an updated value for the iterative variable; finally, repeat the procedure by using the updated iterative variable to the position equations till the prescribed accuracy is obtained. The method proposed has a clear geometric meaning, and the algorithm is simple and direct. Simulation for 100 poses of the end frame shows that the average running time of inverse kinematics calculation for each demanded pose of end-effector is 7.2 ms on an ordinary laptop, which is good enough for practical use. The iteration counts 2-4 cycles generally, which is a quick convergence. The method proposed here has been successfully used in the project of automating a hydraulic rig.

On Newton-Like Methods for Solving Nonlinear Equations

In this paper, we present a family of general New to n-like methods with a parametric function for finding a zero of a univariate fu nction, permitting f′(x)=0 in some points. The case of multiple roots is n ot treated. The methods are proved to be quadratically convergent provided the w eak condition. Thus the methods remove the severe condition f′(x)≠0. Based on the general form of the Newton-like methods, a family of new iterative meth ods with a variable parameter are developed.

Generalized Variational Iteration Solution of Soliton for Disturbed KdV Equation

The corresponding solution for a class of disturbed KdV equation is considered using the analytic method. From the generalized variational iteration theory, the problem of solving soliton for the corresponding equation translates into the problem of variational iteration. And then the approximate solution of the soliton for the equation is obtained.

Response of train-bridge system under intensive seismic excitation by random vibration method

Earthquake is a kind of sudden and destructive random excitation in nature.It is significant to determine the probability distribution characteristics of the corresponding dynamic indicators to ensure the safety and the stability of structures when the intensive seismic excitation,the intensity of which is larger than 7,acts in train-bridge system.Firstly,the motion equations of a two-dimensional train-bridge system under the vertical random excitation of track irregularity and the vertical seismic acceleration are established,where the train subsystem is composed of 8 mutually independent vehicle elements with 48 degrees of freedom,while the single-span simple supported bridge subsystem is composed of 102D beam elements with 20 degrees of freedom on beam and 2 large mass degrees of freedom at the support.Secondly,Monte Carlo method and pseudo excitation method are adopted to analyze the statistical parameters of the system.The power spectrum density of random excitation is used to define a series of non-stationary pseudo excitation in pseudo excitation method and the trigonometric series of random vibration history samples in Monte Carlo method,respectively solved by precise integral method and Newmark-βmethod through the inter-system iterative procedure.Finally,the results are compared with the case under the weak seismic excitation,and show that the samples of vertical acceleration response of bridge and the offload factor of train obeys the normal distribution.In a high probability,the intensive earthquakes pose a greater threat to the safety and stability of bridges and trains than the weak ones.

Exact Solutions of the Harry-Dym Equation

The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He＇s variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation.

Scaling Equation for Invariant Measure

An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.

Newton-EGMSOR Methods for Solution of Second Order Two-Point Nonlinear Boundary Value Problems

The convergence results of block iterative schemes from the EG （Explicit Group） family have been shown to be one of efficient iterative methods in solving any linear systems generated from approximation equations. Apart from block iterative methods, the formulation of the MSOR （Modified Successive Over-Relaxation） method known as SOR method with red-black ordering strategy by using two accelerated parameters, ω and ω′, has also improved the convergence rate of the standard SOR method. Due to the effectiveness of these iterative methods, the primary goal of this paper is to examine the performance of the EG family without or with accelerated parameters in solving second order two-point nonlinear boundary value problems. In this work, the second order two-point nonlinear boundary value problems need to be discretized by using the second order central difference scheme in constructing a nonlinear finite difference approximation equation. Then this approximation equation leads to a nonlinear system. As well known that to linearize nonlinear systems, the Newton method has been proposed to transform the original system into the form of linear system. In addition to that, the basic formulation and implementation of 2 and 4-point EG iterative methods based on GS （Gauss-Seidel）, SOR and MSOR approaches, namely EGGS, EGSOR and EGMSOR respectively are also presented. Then, combinations between the EG family and Newton scheme are indicated as EGGS-Newton, EGSOR-Newton and EGMSOR-Newton methods respectively. For comparison purpose, several numerical experiments of three problems are conducted in examining the effectiveness of tested methods. Finally, it can be concluded that the 4-point EGMSOR-Newton method is more superior in accelerating the convergence rate compared with the tested methods.

Distance-Stability of Nonlinear Discrete Systems

In this paper,the distance-sability of nonlinear discrete system is investigated by means of the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov function is avoided.

Calculation of Combustion Products by the New Iteration Method of Non-linear Equations

For a specific combustion problem involving calculations of several species at the equilibrium state, it is simpler to write a general computer program and calculate the combustion concentration. Original work describes, an adaptation of Newton-Raphson method was used for solving the highly nonlinear system of equations describing the formation of equilibrium products in reacting of fuel-additive-air mixtures. This study also shows what possible of the results. In this paper, to be present the efficient numerical algorithms for. solving the combustion problem, to be used nonlinear equations based on the iteration method and high order of the Taylor series. The modified Adomian decomposition method was applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms. Comparisons of results by the new Matlab routines and previous routines, the result data indicate that the new Matlab routines are reliable, typical deviations from previous results are less than 0.05%.

KSSOLV-GPU:an Efficient GPU-Enabled MATLAB Toolbox for Solving the Kohn-Sham Equations within Density Functional Theory in Plane-Wave Basis Set

KSSOLV(Kohn-Sham Solver)is a MATLAB(Matrix Laboratory)toolbox for solving the Kohn-Sham density functional theory(KS-DFT)with the plane-wave basis set.In the KS-DFT calculations,the most expensive part is commonly the diagonalization of Kohn-Sham Hamiltonian in the self-consistent field(SCF)scheme.To enable a personal computer to perform medium-sized KS-DFT calculations that contain hundreds of atoms,we present a hybrid CPU-GPU implementation to accelerate the iterative diagonalization algorithms implemented in KSSOLV by using the MATLAB built-in Parallel Computing Toolbox.We compare the performance of KSSOLV-GPU on three types of GPU,including RTX3090,V100,and A100,with conventional CPU implementation of KSSOLV respectively and numerical results demonstrate that hybrid CPU-GPU implementation can achieve a speedup of about 10 times compared with sequential CPU calculations for bulk silicon systems containing up to 128 atoms.

Iteration Linear Programming Method and Livestock Ration Optimization

Iterative linear programming methods are proposed for optimum balanced animal diet in this paper. According to ＂wooden bucket theory＂ of the nutritional balance, each nutrient in the feeding standard has equal importance. It＇s unreasonable to use common goal programming to attach different weighted value to different nutritional parameters. This paper introduces an effective algorithm to deal with this kind of problem. When the permitting cost of livestock ration is given, we can design a ration formula with linear program-this is the first round. Then, according to the differences between the permitting cost and the formula cost gained in the first round, adjust the feeding standard and the feeding raw materials, and conduct the second round of linear programming for ration formula. If there is still a very big difference between the formula cost and the permitting cost, the third round will be taken, and so on. In this iteration course the formula cost gradually approaches the permitting cost. It is the key that the feeding standard and feeding raw materials are modified in each round. This method ensured the nutritive equilibrium with the formulation of least-cost ration. This is an especially important method when the primary goal of the optimization tool is to improve economic and nutritive efficiency.

A projection method and Kronecker product preconditioner for solving Sylvester tensor equations

The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper.By fully exploiting the structure of the tensor equation,we propose a projection method based on the tensor format,which needs less flops and storage than the standard projection method.The structure of the coefficient matrices of the tensor equation is used to design the nearest Kronecker product(NKP) preconditioner,which is easy to construct and is able to accelerate the convergence of the iterative solver.Numerical experiments are presented to show good performance of the approaches.