查询词典 matrix norm

In the thesis , firstly the problem of static output feedback H∞control was explored for discrete time singular systems. Based on the generalized Riccati inequality and linear matrix inequality, necessary and sufficient conditions were obtained for the existence of static output feedback H∞controllers, which guarantees that the resulting closed-loop system is admissible with its transfer function matrix satisfying H∞norm constraint.

本文首先利用线性矩阵不等式和广义Riccati不等式，给出离散广义系统中存在静态输出反馈H∞控制器，使得闭环系统是容许的且其传递函数矩阵满足H∞范数约束的充要条件。

Then,a new fast algorithm of the minimal norm least squares solution for linear system whose coefficients is an m×n symmetric Loewner matrix with full column rank is given by forming a special block matrix and researching the triangular factorization of its inverse.

对于工程计算中常常遇到的一类线性方程组的求解，通过构造特殊分块矩阵并研究其逆矩阵的三角分解，给出了求秩为n的m×n阶对称Loewner矩阵为系数阵的线性方程组，及极小范数最小二乘解的快速算法，该算法的计算复杂度为O+O(n2)，而一般方法的计算复杂度为O(mn2)+O(n3)。

The conventional matrix decomposition methods have been used to find the least-squares solutions of the abovementioned inconsistent matrix equations over given matrix set in many references, and the general expressions of these solutions were obtained. But it is difficult to determine the solution of Problem I by utilizing these expressions due to the fact that the orthogonal invariance of Frobenius norm does no hold for the general nonsingular matrices.

对于求上述不相容矩阵方程在给定矩阵集合上的最小二乘解，很多文献中利用传统的矩阵分解方法得到了其通解表达式，但是利用该表达式很难得到问题Ⅰ的解，这是因为一般的非奇异矩阵并不满足Frobenius范数的正交不变性。

The matrix operator norm and unitarily invariant norm are two important normclasses.

0引言矩阵的算子范数和矩阵的西不变范数是两大类不同的重要范数类。

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。

From the main results, when the spectral norm of the system matrix is less than 1 or the matrix induced by the system matrix is Schur, the fuzzy system is asymptotically stable.

主要结论指出，当系统矩阵谱范数小于1或系统矩阵的诱导矩阵是Schur矩阵时，模糊系统全局渐近稳定。

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。

For any initial generalized bisymmetric matrix $X_1$, when $AXB=C$ is consistent, we can obtain the generalized bisymmetric solution of the matrix equation AXB=C within finite iterative steps by the iteration method in the absence of roundoff errors; Moreover, the least-norm solution $X^*$ can be obtained by choosing a special kind of initial generalized bisymmetric matrix.

在不考虑机器误差的情况下，当矩阵方程AXB=C相容时，对任意广义双对称X_1，矩阵方程AXB=C的解可以经过有限步迭代得到；特别地，通过选择特殊地初始广义双对称矩阵极小范数解X^*。

When the matrix equation is consistent, its centrosymmetric solution can be obtained within finite iterative steps in the absence of round off errors for any initial centrosymmetric matrix X1, and its least-norm centrosymmetric solution can be derived by choosing a suitable initial iterative matrix.

当矩阵方程AXB+CXD=F有中心对称解时，在有限的误差范围内，对任意初始中心对称矩阵X1，运用迭代算法，经过有限步可得到矩阵方程的中心对称解；选取合适的初始迭代矩阵，还可以迭代出极小范数中心对称解。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。