矩阵范数

Linear memoryless state-feedback control law is derived for two classes of uncertain nonlinear interconnection systems with sector restriction or norm-bounded restriction based on Linear Matrix Inequality. This method doesn't require that two input terms are absolutely controllable for nonlinear delay systems.

基于线性矩阵不等式分别导出了具有扇形角约束和范数有界约束的两类非线性关联不确定系统的线性无记忆状态反馈控制律设计方法，该方法不要求系统的两输入项对系统完全可控。

A important result is the one-order expression of AR Yt = DYt-1 + E, from paralleling a high-order differential equation transformation into a one-order differential equation system, the one-order expression exposes that the AR is only a certain more-multivariable power series processAnd, if a process is described as an AR, the sufficient and necessary condition is the spectrum norm A of the coefficient matrix D less than one.

作者用高阶微分方程化一阶微分方程组的方法，获得多元弱平稳序列p阶自回归模型的一步滑动平均表达式，证明了AR的是一个更高维的幂级数的线性过程，从而，说明了AR关于序列依概率成立的充要条件是：该模型更高维的幂级数的线性过程的表达式中系数矩阵D的谱范数λ＜1。

The parallel computing of the preconditioner is the bottleneck for the parallel computing of Krylov Subspace Methods. Based on norm-minimization technique, a parallel sparse approximate inverse preconditioning method is present for the unsymmetric sparse linear systems.

7预条件子的并行计算是利用Krylov子空间方法进行并行计算的瓶颈，我们利用矩阵的Frobenius范数，提出了一种构造一般非对称稀疏线性方程组预条件子的PPAT方法，该方法具有天然的并行性。

The second part includes the definition of positive definite function and conditional positive definite function, the basic form of Radial Basis Function interpolation, the correctness of the inversion of the interpolation matrix, the error estimate based on Kringing function.

主要包括径向基函数的相关定义，基本的插值形式，插值矩阵的可逆性，以Kringing范数为基础的径向基函数插值的局部误差估计和径向基函数插值边界附近的情况。

In the optimal control of kinematics for redundant robots, two new concepts, the matrix weightability measure and the self-motion declinability measure are proposed. Further, a modified weighted gradient projection method which combines gradient projection method with weighted least-norm solution is presented, it can attain ideal optimal effects at low velocities.

本文对冗余自由度机器人的运动学、动力学和容错等方面的优化控制进行了深入的分析和探讨：在冗余度机器人运动学优化控制方面，提出矩阵可加权度和自运动可衰度的概念，将梯度投影法和加权最小范数解法有机的相结合，形成可优化能力强、关节速度较低的改进的加权梯度法。

Using the singular value decomposition of matrix, the uncertain fuzzy systems can be united to the model with norm-bounded structure parameter uncertainties.

利用矩阵奇异值分解和线性变换，将不确定性模糊系统归一化为具有界范数约束的结构参数不确定性的模糊系统模型。

First, various normwise relative condition numbers that measure the sensitivity of W-weighted Drazin inverse and the solution of singular linear systems are characterized.

首先，我们利用不同的范数定义了加权Drazin逆及其奇异线性方程组解的条件数，用来度量矩阵求加权Drazin逆和一类奇异线性方程组求加权Drazin逆解对于扰动的敏感性。

About weight Linear regression model,We propose the problem of influence measure of weight disturbance,provide the maritx of influence measure of weight disturbance,and utilize trace aud spectral norm,at last,get some results.

对于加权线性回归模型，我们考虑权扰动的影响度量问题，给出权扰动的影响度量矩阵，利用迹、谱范数为工具，得出一些结论

Fast algorithms for the minimal norm least square solutions of linear equations which coefficients are m×n Toeplitz matrix are given.

给出了求以m×n阶Toeplitz矩阵为系数阵的线性方程组极小范数最小二乘解的快速算法。

The main elements affecting load coupling characteristics among channels were analysed based on joint space dynamics equations of Stewart platform, and four kinds of load coupling evaluation index were presented with the matrix and vector norm theory.

基于Stewart平台关节空间动力学方程，分析了影响通道间负载交联耦合的主要因素，采用矩阵和向量范数理论提出了4种负载交联耦合评价指标。

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。