Fourth-order accurate BLAGE iterative method for the solution of two-dimensional elliptic equations in polar co-ordinates

In this article, we report on the block alternating group explicit (BLAGE) iterative method for solving the block symmetric linear system derived from the fourth-order accurate nine-point discretisation of a two-dimensional elliptic equation in cylindrical polar co-ordinates. The error analysis of the BLAGE method is discussed briefly. The performance of this more accurate BLAGE method is compared with the corresponding block successive over relaxation (BSOR) method by considering two test problems, wherein the significance of the role played by two parameters ω₁ and ω₂ of the BLAGE method becomes evident in providing both convergence and accuracy of the computed solution.     

A weighted H1 seminorm regularization method for Fredholm integral equations of the first kind

Many problems in mathematics and engineering lead to Fredholm integral equations of the first kind, e.g. signal and image processing. These kinds of equations are difficult to solve numerically since they are ill-posed. Therefore, regularization is required to obtain a reasonable approximate solution. This paper presents a new regularization method based on a weighted H¹ seminorm. Details of numerical implementation are given. Numerical examples, including one-dimensional and two-dimensional integral equations, are presented to illustrate the efficiency of the proposed approach. Numerical results show that the proposed regularization method can restore edges as well as details.     

Convergence of a parallel jacobi-type method

A relaxed Jacobi-type iterative scheme is presented for solving linear algebraic systems. The method possesses a high level of parallelism and can be implemented on a multiprocessor system with or without synchronisation. The convergence region of the relaxation parameter is determined under the condition that the Jacobi iteration matrix possesses real eigenvalues. However, when the method is applied to consistently ordered systems, it is preferrable to let the parameter equal to unity and use Conjugate Gradient methods [3] to further increase the convergence rate.     

考虑避碰约束的编队卫星入网路径规划

提出了一种新的考虑避碰约束的编队卫星入网路径规划策略。首先通过常规编队卫星入网的多脉冲线性规划方法,得到一组卫星入网的脉冲序列,以此预测轨道机动过程中各星之间的最小距离,当最小距离小于安全距离时,将最小距离前后脉冲施加时刻的相对位置作为约束条件,重新规划卫星入网轨迹,迭代进行直到满足避碰要求。仿真结果表明,该方法由于减少了路径规划过程中约束条件的个数,能够快速地规划出考虑避碰约束时的编队卫星入网轨迹,且有效节省燃料消耗。     

U形断面渠道收缩水深迭代计算初值的研究

对U形断面收缩水深的基本方程进行恒等变形,通过优化拟合分析得到了收缩水深的迭代公式,再与合理的迭代初值配合使用,迭代结果快速收敛。在工程常用范围内,只需一次迭代即可使最大相对误差小于0.50%。误差分析及实例计算表明,收缩水深的迭代计算公式形式简捷、精度高、适用范围广。     

Parallelizable restarted iterative methods for nonsymmetric linear systems. part I: Theory

Large sparse nonsymmetric problems of the form A u = b are frequently solved using restarted conjugate gradient-type algorithms such as the popular GCR and GMRES algorithms. In this study we define a new class of algorithms which generate the same iterates as the standard GMRES algorithm but require as little as half of the computational expense. This performance improvement is obtained by using short economical three-term recurrences to replace the long recurrence used by GMRES. The new algorithms are shown to have good numerical properties in typical cases, and the new algorithms may be easily modified to be as numerically safe as standard GMRES. Numerical experiments with these algorithms are given in Part II, in which we demonstrate the improved performance of the new schemes on different computer architectures.     

规范状态空间系统辨识方法

因为状态空间模型既包含了未知状态,又包含了未知参数,且二者是非线性乘积关系,使得辨识问题变得复杂.针对这一问题,详细研究了规范状态空间系统的状态与参数联合估计方法.采用交互估计理论,即采用递推方法或迭代方法实现系统状态与参数的交互估计.基本思路是在计算参数估计时,辨识算法信息向量中的未知状态用其估计值代替,然后利用获得的参数估计,设计基于参数估计的状态观测器或基于参数估计的Kalman滤波算法估计系统的状态,二者形成一个交互计算过程(递阶计算过程).沿着这条思路,分别从递推方案和迭代方案,研究和提出了基于状态观测器和基于Kalman滤波状态估计的随机梯度辨识算法、递推最小二乘辨识算法、多新息随机梯度辨识算法、多新息最小二乘辨识算法,以及模型分解的辨识算法,并给出了几个典型算法的计算步骤、流程图和计算量.     

扫描光刻系统的分段迭代学习控制策略

结合扫描光刻系统的曝光特点,提出一种分段迭代学习控制方法.该方法继承了非因果迭代学习律充分学习的特点.为改善动态跟踪性能,在加速过程段对前一迭代周期的误差信息进行非因果学习,以保证其沿迭代轴的快速收敛性.为克服非因果迭代学习律盲目学习的缺点,在匀速曝光段不对误差信息进行非因果学习,以保证系统的曝光性能不发生恶化,并改善系统在时间轴的瞬态性能.此外,对该方法的收敛性进行了分析和证明,并结合实例,验证了方法的有效性.     

非周期时变非线性系统自适应迭代学习控制

对一类含有非周期时变不确定性的非线性系统的控制问题进行了研究。该系统具有严格反馈形式且控制增益未知。在控制器设计中,用一种具有迭代特性的神经网络消除了非周期时变不确定性的影响,并综合应用反演技术和鲁棒自适应控制技术消除了严格反馈结构和未知控制增益带来的设计问题。稳定性分析结果表明:系统所有状态量有界且输出量在积分意义下收敛到期望轨迹。仿真试验证明了所设计控制器的有效性。     

井地地震技术数值模拟及工程应用

井地地震是通过地面激发,井中接收的方式来对目标体进行透视的物探技术,该技术利用地震波走时和能量衰减来反演目标体内部结构,解决实际工程问题.本文首先阐述井地地震独特的观测方式及其原理,然后建立地质模型,采用射线追踪法计算走时,应用同时迭代重建算法(SIRT)进行数值模拟,并分析该算法的效率和精度,总结其优缺点,最后通过某...