Global and local superlinear/quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs.
基于此给出了求解箱约束变分不等式的一种阻尼牛顿算法，在较弱的条件下，证明了算法的全局收敛性和局部超线性收敛率，以及对线性箱约束变分不等式的有限步收敛性。
A damped Newton type method was presented based on it. Global and local superlinear/quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs.
基于此给出了求解箱约束变分不等式的一种阻尼牛顿算法，在较弱的条件下，证明了算法的全局收敛性和局部超线性收敛率，以及对线性箱约束变分不等式的有限步收敛性。
Response surface approximate functions were optimized by using multidisciplinary design feasible and sequential response surface methods were adopted to avoid much of computing time consume in the traditional optimization method and slow convergence or no convergence in the non- linear impact and NVH systems.
避免了传统整车耐撞性和白车身NVH相结合的多学科优化设计方法计算量大，且在碰撞非线性系统优化中常常易导致收敛缓慢甚至不收敛的缺点。
The characteristics of the steepest descent method's small amount of computations and conjugate direction method's fast convergence combined, a conjugate vector base method for solving ill-conditioned linear equations was proposed.
结合最速下降法计算量小和共轭方向法收敛速度快的特点，提出了一种求解病态方程组的共轭向量基的方法。
The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet, show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O, where N is the order of matrix.
理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。
Mixed linear complementarity, Multiplier method, Global convergence, Finite termination property.
混合线性互补，乘子法，全局收敛，有限步收敛
The linear elastic adaptive FEM calculation results show that the stress singularity of dam heel doesn`t affect the convergence of adaptive computation, the different original grids and control parameters of mesh size can achieve the approximate results, satisfactory result is obtained if the appropriate energy error limit is adopted, and the stresses at dam heel zone converge to the stable values.
算例表明，自适应计算不会因角缘应力集中而出现剖分不收敛情况，且计算结果不受初始网格和单元尺寸改变控制因子影响；存在一个稳定的临界全域能量误差限，超过该值后，继续降低误差限，坝踵区的应力趋于稳定值，且不随坝高和弹模比的改变而变化。
This algorithm is a linear method, its identifiability and convergence is verified.
这一算法是一线性辨识算法，其收敛性容易得到满足。
Based on the paper〔1〕, give LF topology definited LF pre-norm to the concept of closed set into LF pre-norm al space with the theory of convergence of molecular net, and discuss relative properties and prove that LF pre-norm al space is a special LF topology linear space.
在文〔1〕的基础上，用分子网的收敛理论，对LF赋准范空间引入闭集的概念，给出了LF准范数所确定的LF拓扑，并讨论了有关性质，证明了LF赋准范空间是一类特殊的LF拓扑线性空间，从而，为探讨LF拓扑线性空间可LF赋准范化问题打下了良好的基础。
The sensor error compensation method based on orthogonal basis neural network algorithm has high accuracy of compensation, small calculated amount and fast convergence rate. It has significant advantages compared with the best linear fit, the least-squares polynomial curve fitting, nonlinear inverse function compensation, and other nonlinear neural network compensation methods. Therefore it is an effective method of sensor error compensation.
基于正交基神经网络算法的传感器误差补偿方法具有高的补偿精度，计算量小，收敛速度快，与最佳直线拟合法、最小二乘法多项式曲线拟合法、非线性反函数补偿法以及其它神经网络的非线性补偿等方法相比具有明显的优势，因而是一种有效的传感器误差补偿方法。
The research methods and achievements about the incompatible mode geometrically non-linear FEM in China are reviewed, which include: 1 a convergence criteria of incompatible mode geometrically non-linear FEM was proposed based on Hellinger-Reissner generalized variational principle, and the simplified model of incompatible geometrically non-linear FEM was constructed by using some simplified methods; 2 a class of non-linear generalized variational principles was proposed, in which the compatible conditions between elements are relaxed. The incompatible models can be constructed by selecting incompatible functions without satisfying compatible conditions prior and the convergence can be guaranteed. The C1 or C0 geometrically non-linear generalized hybrid elements, C1 or C0 refined hybrid elements and directly refined stiffness methods can be constructed by applying the non-linear generalized variational principles.
介绍了国内学者关于几何非线性非协调模式的研究方法和研究成果：(1)从Hellinger-Reissner 广义变分原理出发，提出了几何非线性非协调模式的收敛条件，并采用非线性计算的若干简化措施建立几何非线性非协调元的简化模型；(2)一类放松单元间协调要求的非线性广义变分原理，对几何非线性问题可以选择事先无协调约束的非协调函数建立非协调元，收敛性可以保证，并根据此非线性广义变分原理可建立C$^1$或C$^0$类几何非线性广义杂交元，C$^1$或C$^0$类精化杂交元和精化直接刚度法。
Order Hilbert ill-conditioned linear equations were solved, and the relative error was less than 0.45%. Numerical experiments verified that the method was efficient compared with the efficient methods used commonly nowadays. Numerical experiments results showed that the conjugate vector base method was suited for solving large-scale ill-conditioned linear equations with fast convergence and high precision.
通过对5000阶的Hilbert方程组进行求解，结果的相对误差小于0.45%，并与当前普遍使用有效的方法进行了比较，数值实验结果表明，该算法适合求解大型病态线性方程组，且具有快速收敛，精度较高的特性。
In Chapter 3, we consider a direct search method for a class of linear equality constrained optimization problems, which makes use of grids called grid-based methods, and give a proof of its convergence.
主要工作是给出了解这类线性等式约束优化问题的一种新的方法，即直接搜索方法中的格子基搜索算法，并且证明了这个算法的收敛性。
According to the non-linear characteristic of the transmission line, this paper used the convergence factor to adjust the course of iteration.
根据导线结构的非线性特点，采用了收敛因子来调整迭代过程。
For solving the singular linear equations, we present the iterative methods based on proper splittings and give the convergence analysis.
在奇异线性方程组的求解方法中，我们提出了基于正则分裂的二级迭代法并给出收敛分析；在论文的第三章我们对奇异的结构化矩阵的置换秩进行了研究，得到了一些结论并给出了应用。
The resulting linear system, the coefficient matrix of which is, typically, a 2 x 2 block symmetric or non-symmetric and singular or non-singular indefinite matrix, is of high order and ill conditioned. In order to solve such system we have to use iterative methods with fast convergence speed.
所得的离散方程组（其系数矩阵典型地是 2 x 2 块对称或非对称，奇异或非奇异的不定矩阵）是高阶和病态的，为了求解这样的方程组我们必需使用快速收敛的迭代方法。
In Chapter 3 Firstly, the exponential stability in mean square and almost sure exponential stability for neutral stochstic neural networks with time-varying delay can be discussed by using the linear matrix inequality and the semimartingale convergence theorem; And our sufficient conditions are less conserative; Secondly, by utilizing the fixed point theorem, some sufficient and necessary conditions ensuring the asymp- totic stability in mean square for neutral stochastic neural networks with time-varying delays can be given.
第三章首先，利用线性矩阵不等式方法和半鞅收敛定理，考虑了一类具变时滞中立型随机神经网络的二阶矩指数稳定性和几乎必然指数稳定性，所得到的条件保守性要好；其次，采用不动点方法，给出了具变时滞中立型随机神经网络的二阶矩渐近稳定性的充要条件。
The identification ofobject is easy to trap in local minimum, Radical basic Function network, because therelation between network and output is linear, so we can adopt the method which assureglobal convergence and get the globally optimal solution, but it is difficult to choose thecenter point.
用BP网络进行辨识容易陷入局部极小点问题，径向基函数网络因为网络权值与输出呈线性关系，所以可采用保证全局收敛的线性化学习方法，并可获得全局最优解，但其应用难点是中心点的选择不易。
At the beginning of this paper, we briefly introduced the fundamental knowledge of the Newton iterative methods, and the local convergence theorem which extended the classical Newton method, because of the local convergence, the theorem had its certain restrict. Large-scale convergence theorem was proved under the condition that matrix M is irreducible diagonally dominant by Newton's method with line search. At the last part of this paper, we present the method for solving linear complementarity problems arising from journal bearings.
本文首先介绍了Newton型迭代法的基础知识，然后着重介绍了B-可微方程的Newton法，给出B-可微法的局部收敛结论，推广了古典的Newton法，但由于收敛的局部性，该算法仍有一定的不足之处；文章在证明大范围收敛定理时，假设M是不可约对角优势矩阵，采用一维Newton寻查的方法，保证算法的收敛性。
Numerical experiment of eight elements` uniformly-spaced linear array using this algorithm is performed. Computer simulations show that immuning algorithm can suppress the sidelobe effectively. A lower max sidelobe which compared with simple genetic algorithm is gained. The pace of convergence is also excellent.
对八阵元组成的等间距直线阵进行了数值实验，仿真结果表明，该算法能有效地抑制直线阵左右最大旁瓣，获得了比基本遗传算法更低的最大副瓣，并且收敛速度明显优于基本遗传算法。