非数值算法

Chapter 9: We report a large quantity of numerical experiments of 13 different algebraic multigrid algorithms for solving the Poisson equation, anisotropic equation, equation with cross-derivative terms, general matrix problems with large off-diagonal positive entries, biharmonic equation, Toeplity matrix, elasticity systems, finite element discretization of the Laplacian and even 3D problems. Particular attention is focused on asymptotic convergence factors and CPU-time consumed. Numerical results for many different types of practical problems demonstrate the efficiency and robustness of the proposed algebraic multigrid methods.

第九章：在各种代数多重网格算法的基础上，进行了大量的数值试验，具体给出了十三种不同的代数多重网格方法求解泊松方程，各向异性方程，带混合导数项的方程，带有大的非对角正元素的一般矩阵问题，重调和方程，托普利兹矩阵，弹性力学方程组，拉普拉斯算子的有限元离散，甚至三维问题的较为丰富的数值结果，重点关注它们的渐近收敛因子和所需的CPU时间，来源于不同类型问题的计算结果既为代数多重网格理论分析和算法的改进提供了很实用的资料，同时也证实了本文给出的代数多重网格算法的效绩和稳健性。

Furthermore, the first-order optimality condition and its equivalent reformulations for generalized semi-infinite max-min programming with a non-compact set are presented using the lower-Hadamard directional derivative and subdifferential.2. Chapter 3 studies the gradient-type methods for unconstrained optimization problems. Section 1 proposes a new class of three-term memory gradient methods. The global convergence property of the method is established. Furthermore, in order to improve the convergence property of the method, a new class of memory gradient projection methods is presented with the property that the whole sequence of iterates converges to a solution to the problem under the conditions such as pseudo-convexity and continuous differentiability of objective function. In section 2, two new classes of methods, called gradient-type method with perturbations and hybrid projection method with perturbations, are proposed. In these methods, non-monotone line search technique is employed, which makes them easily executed in computer.

第3章研究了无约束优化问题的梯度型算法，第1节提出了一类新的三项记忆梯度算法，讨论了算法的全局收敛性，进一步提出了一类新的具有更好收敛性质的记忆梯度投影算法，并证明了该算法在函数伪凸的情况下具有整体收敛性，第2节在非单调步长搜索下提出了带扰动项的梯度型算法及其混合投影算法，这两类算法的一个重要特征就是步长采用线搜索确定而不象许多文献中那样要求步长趋于零，这样更容易在计算机上实现，在较弱的条件下证明了这些算法的全局收敛性，数值算例表明了算法的有效性。

Key words:the three dimensional contact problem with friction;nonlinearcomplementary;nonsmooth equations;generalized derivative;nonsmoothmethod;convergence analysis

给出了三维摩擦接触问题的一个非光滑混合不动点模型及算法，这种算法无须求导数，没有引进任何额外变量，并且可视为一种三维摩擦接触问题的迭代法，利用非光滑分析和不动点理论对算法做了分析，给出了算法的不动点理论背景及算法的理论分析，为模型解的存在性及算法收敛性提供分析依据，最后给出了相应的数值算例。

The reconstruction problem is ill-posed, so two optimal criterions, the least module and the smoothness criterion base on Tikhonov regularization technique, are introduced into reconstruction algorithm. Many regularization parameters choice strategies are investigated, and the TPA(Two—Parameter Algorithm) strategy which is based on the Morozov discrepancy principles, is implemented in two regularization reconstruction algorithms.Numerical experiment results show that the nonnegative and smoothness constraint condition can overcome the difficulty of iteration semiconvergent, preconditioned technique can improve convergence rate and reconstruction accuracy, smoothness regularization criterion can meliorate ill-posed problem of reconstruction and enhance iteration stability, and the TPA is an effective strategy of regularization parameters choice.

数值试验表明：在共轭梯度法中引入非负约束和光滑约束改善了迭代的"半收敛"性，非负约束保证了解的非负性，光滑约束抑制了重建解的振荡现象，约束算法的重建精度与无约束算法相比大幅度提高；在约束共轭梯度重建算法中引入预优技术，可以加快算法的收敛速度，提高迭代的稳定性和重建精度；引入光滑准则的正则化技术可以有效改善图像重建问题的不适定性，加快迭代的收敛速度，提高迭代的稳定性和图像重建质量，计算正则参数的TPA算法在闪光照相图像重建中是有效的。

This paper presents an approach for automatic test data generation of non-numeric variables based on genetic algorithms, defines a path fitness function and a character fitness function, and describes a corresponding test data generating process in detail.

本文提出了一种基于遗传算法的非数值型软件测试数据自动生成的方法，定义了路径适应度函数和字符适应度函数，并详细描述了测试数据生成过程。

Aiming to the two points of data compressing and characteristic distilling during the pretreatment of image data process, this paper introduces a non-numeric parallel algorithm of continous hopfield neural network used to clustering of image data mining.

针对图像数据预处理中的数据压缩和特征提取两个重点，介绍一种基于连续Hopfield神经网络的非数值并行算法应用于图像数据挖掘的聚类预处理过程。

Design Krylov subspace conjugate residual squared algorithm for nonsym-metric linear systems and the improved conjugate residual squared algorithm for distributed parallel computing based on biconjugate residual method algorithm, and give theoretical analysis and comparisons of algorithms for two algorithms.

基于BiCR算法设计了求解非对称线性方程组Krylov子空间平方共轭残差算法和适合分布式并行计算的改进的平方共轭残差算法，并对两种算法进行了理论分析和算法比较，串行和并行数值试验表明所提方法具有较好的收敛速度和并行性能。

The multiresolution time-domain algorithm based on the scaling function of the Daubechies wavelet is introduced, and the perfectly matched layer absorbing boundary condition for the algorithm is deduced. In order to overcome the difficulties due to the nonlocalized property of the MRTD basis functions, the pure scattered-field formulation is adopted. The method presented is applied to the scattering analysis of multiple conducting objects, and the numerical results are compared with those by the traditional finite-difference time-domain method. It is shown that the computational resource is reduced drastically without sacrificing much accuracy.

对基于Daubechies小波尺度函数的时域多分辨分析算法进行了详细论述，推导了MRTD算法的完全匹配层吸收边界条件，为克服传统MRTD方法中基函数存在着非局部性的缺点，在源的加入上采用了纯散射场方法；并应用该算法对多目标的电磁散射特性进行了分析，数值结果表明，MRTD算法与传统的时域有限差分法结果相吻合，大大节约了计算资源。

The reconstruction problem is ill-posed, so two optimal criterions, the least module and the smoothness criterion base on Tikhonov regularization technique, are introduced into reconstruction algorithm. Many regularization parameters choice strategies are investigated, and the TPA(Two—Parameter Algorithm) strategy which is based on the Morozov discrepancy principles, is implemented in two regularization reconstruction algorithms.Numerical experiment results show that the nonnegative and smoothness constraint condition can overcome the difficulty of iteration semiconvergent, preconditioned technique can improve convergence rate and reconstruction accuracy, smoothness regularization criterion can meliorate ill-posed problem of reconstruction and enhance iteration stability, and the TPA is an effective strategy of regularization parameters choice.

数值试验表明：在共轭梯度法中引入非负约束和光滑约束改善了迭代的&半收敛&性，非负约束保证了解的非负性，光滑约束抑制了重建解的振荡现象，约束算法的重建精度与无约束算法相比大幅度提高；在约束共轭梯度重建算法中引入预优技术，可以加快算法的收敛速度，提高迭代的稳定性和重建精度；引入光滑准则的正则化技术可以有效改善图像重建问题的不适定性，加快迭代的收敛速度，提高迭代的稳定性和图像重建质量，计算正则参数的TPA算法在闪光照相图像重建中是有效的。

Finally the numerical results are presented to confirm the effectiveness of Gauss-Seidel parallelized with alternate tiling method,specifically compared with owner-computing and red-black Gauss-Seidel methods,and show that the new parallel iterative method has better parallel efficiency as well as scalability.

许多物理应用问题的求解都归结为求微分方程数值解，其核心是高效地求解线性方程组，GS(Gauss一Seidel)和SOR迭代算法以其高效性和实现简单的特性成为大型线性方程组求解的重要算法，并且常用作非定常迭代算法的高效预条件子，是许多应用软件的核心算法之一。在并行处理系统

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。