查询词典 norm of a matrix

The least norm solutions of symmetric and skew antisymmetric matrix equations (A~TXA, XA — YAD)=(D, 0)are also considered. 3. The least-squares solutions and the least norm solutions of the quaternion matrix equations AX = B and XD = E are studied by using

借助四元数的复表示方法，研究四元数矩阵方程组AX=B，XD=E的最小二乘问题和极小范数解的问题，并对主子阵约束下的方程组的解进行了讨论，得到了它们的显式表示。

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)。

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

通过构造特殊分块矩阵及其三角分解给出了求秩为n的m×n阶Loewner型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，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)。

In Chapter three, by constructing a special partitioned matrix and studying the fast triangular factorization of its inverse matrix, we respectively give fast algorithms for the minimal norm least squares solutions of linear equations which coefficient matrices are n×m Toeplitz type matrices and Vandermonde-Loewner type matrices with full column rank.

第三章通过构造特殊分块矩阵并研究其逆矩阵的快速三角分解，分别给出了求以秩为m的n×m阶Toeplitz型矩阵和Vandermonde-Loewner型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，并通过算例将新算法与已有的法方程组的方法和正交化方法作了比较。

An equivalent condition for the singular discrete linear systems to be regular, causal, stable as well as the transfer function satisfying a prescribed H-infinity norm bound is obtained by means of linear matrix inequation method.

利用线性矩阵不等式方法，导出广义离散线性系统正则、因果、稳定且传递函数满足给定的范数界的等价条件。

By the definition and properties of matrix norm, a corollary expressed by matrix norm is obtained.

又利用矩阵范数的定义及性质，得出了一个以范数形式表示的推论。

The decentralized impulse control of a class of large-scale interconnected uncertain descriptor systems is studied by use of Lyapunov method and matrix norm properties.

考虑了一类不确定广义关联大系统，利用Lyapunov方法和矩阵范数性质研究了该类系统的分散脉冲控制问题。

The new updating method is to minimize the error matrix norm under the condition of a quadratic constraint under which the mode orthogonality should be satisfied and the mass and stiffness matrices should be fitted into the eigen equation.

该方法是在质量矩阵和刚度矩阵满足正交性条件和特征方程的约束下，使修正矩阵的范数最小，将模型修正问题转化为一个带二次约束的最小二乘问题。

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。

In chapter two, we first consider the linear system WAWx=b, where A is an m*n rank-deficient matrix. Then we consider the weighted Frobenius norm on data, and get the formula of W-weighted Drazin inverse solution of the linear system.

第二章的前半部分介绍了线性系统 WAWx=b 的加 W 权的 Drazin 逆解在范数带参数的 Frobenius 范数意义下的条件数，这里矩阵 A 为一个 m*n 的秩亏阵。

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。