查询词典 norm of a matrix

By exploiting the important properties of robot dynamics, the second strategy removes the requirement of a priori bound on parametrer uncertainty and weakens the restriction on external disturbance. The only requirement is to know an upper bound of the norm of inertia matrix, which is not necessary to be the smallest.

第二种算法利用机器人固有的结构特性，减弱了目前已有文献对未建模扰动的限制，它不要求预先知道机器人结构参数的不确定范围，仅要求已知实际惯量矩阵范数的一个上界。

Fast algorithm of minimal norm least square solution for Cauchy linear system;2. For the m×n Cauchy-type matrix with full column rank,the fast algorithm of the minimal norm least square solution to the linear system Cx=b was obtained by construction of a special block matrix and study of the triangular decomposition.

对于秩为n的m×n阶Cauchy型矩阵C，通过构造特殊分块矩阵并研究其三角分解，进而得到了线性方程组C x=b的极小范数最小二乘解的快速算法，所需运算量为O+O(n2)，而通常构造法方程组的方法所需运算量为O(m n2)+O(n3)，用正交化法虽然避免了构造法方程组，但所需的运算量更大些。

For the latter, we present a concept of unitizing the norm of sliding matrix to optimize the control law design such that the control cost is limited.

另外，对新近发展起来的滑模面系数匹配情况，给出了静态输出反馈下的结论，但该结论的求解是享有方法无法直接求解的。

It is proved by means of constructing the new norm of the vector and the norm of matrix that the Runge-Kutta method is H-stable if|R | and A is nonsingular.

我们构造了一个新的向量范数和矩阵范数，利用该范数证明了如下定理，如果|R|和矩阵A非奇异，则Runge-Kutta方法是H-稳定的。

The preface gave the definition and introduced history, background of development and significance of generalized inverse matrix. The first chapter, from the development process of generalized inverse, discussed all kinds of definition of generalized inverse determined by the Moore - Penrose equations. The second chapter discussed the definition and nature of dashes inverse A in generalized inverse as well as its application in compatible linear equations. The third chapter discussed the definition and calculation of the minimum norm inverse A in generalized inverse, as well as the Minimal Norm Solution of its compatible linear equations Ax = b.

前言从引进广义逆矩阵的定义着手，介绍了它的历史概况以及发展的背景及其意义；第一章从广义逆的发展历程讨论由Moore-Penrose方程确定的各种广义逆的定义；第二章讨论广义逆中的减号逆A 的定义及性质以及在相容线性方程组的应用；第三章讨论广义逆中的最小范数逆A 的定义及计算以及它与相容线性方程组Ax=b的极小范数解。

Exive least-squares solutions, antire?exive least-squares solutions, bisymmetric least-squaressolutions, symmetric and antipersymmetric least-squares solutions, symmetric or-thogonal symmetric least-squares solutions, symmetric orthogonal antisymmetricleast-squares solutions and their optimal approximation to the linear matrix equa-tion AX = B, and solve them successfully. 2. For Problem II, we can convert it to another problem of finding the least-squares solutions with the least norm of a new consistent matrix equation. Onthe base of the solutions of Problem I we can apply the iterative method to get

本文所构造的迭代法的优点在于先利用法方程变换将求矩阵方程的最小二乘解转化为求一个相容矩阵方程的解的问题，再利用迭代法对于任意给定的初始矩阵进行迭代，均可在有限步内迭代出所求问题的一个解；可将问题II转化为求新方程的极小范数解的问题，同样用迭代法求解，从而系统且全面地解决了问题I、II在约束矩阵类如中心对称、中心反对称、自反矩阵、反自反矩阵、双对称、对称次反对称、对称正交对称、对称正交反对称矩阵中的最小二乘解及其最佳逼近问题。

The method of estimation in paper [7] is to build fitness function by the 2-norm of error matrix directly. For the error matrix is a Toeplitz matrix, a novel fitness function was presented. Then a new method, the real-valued genetic algorithm which is based on genes weights variation independently, is developed in this paper.

文献[7]提出的估计方法直接以误差矩阵的2范数建立适应度函数，文中利用该矩阵是Toeplitz矩阵的特性，构造了一个新的适应度函数，提出了一种基于基因分量独立变异的实数遗传算法。

Furthermore,the optimal approximation bisymmetric solution pair to a given bisymmetric matrix pair in Frobenius norm can be obtained by finding the least norm bisymmetric solution pair of new matrix equation ,where .

另外，给定双对称矩阵对，通过求矩阵方程的双对称解对，得到它的最佳逼近双对称解对。

A numerical algorithm and a numerical experiment are given. 2. The least norm, positive semidefinite and positive definite real solutions of bisymmetric matrix equations (A~TXA, XA — YAD)=(D, 0)are considered by applying the generalized singular value decomposition.

利用广义奇异值分解讨论了矩阵方程(A~T XA，XA-YAE)=(E，0)在对称次反对称矩阵集合中的解、极小范数解和在双对称矩阵集合中的解、极小范数解及正定解； 3。

In addition, the unique optimal approximation solution $\\\\\\\\\\\\\\\\hat X$ to given matrix $X_0 $ in Frobenius norm can be derived by finding the least-norm generalized bisymmetric solution $\\\\\\\\\\\\\\\\widetilde X^\\\\\\\\\\\\\\\\ast$ of the new matrix equation $A\\\\\\\\\\\\\\\\widetilde X B=\\\\\\\\\\\\\\\\widetilde C$, here,$\\\\\\\\\\\\\\\\widetilde X=X-X_0$, and $\\\\\\\\\\\\\\\\widetilde C=C-AX_0B$.

另外，对于给定矩阵X_0的最佳逼近解$\\\\\\\\\\\\\\\\hat X$，可以通过求解新的矩阵方程$A\\\\\\\\\\\\\\\\widetilde X B=\\\\\\\\\\\\\\\\widetilde C$得到，其中$\\\\\\\\\\\\\\\\widetilde X=X-X_0$，$\\\\\\\\\\\\\\\\widetilde C=C-AX_0B$。

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。