查询词典 norm of a matrix

By means of analyzing the noise error, it is proposed to use an algorithm of singular value decomposition total least squares to conduct the interharmonics estimation, namely taking the noise interference at both sides of the matrix equation into account simultaneously and solving the minimum norm problem by least square method under such condition. In the proposed algorithm by means of singular value decomposition of a new augmented matrix and by use of a simple and practical method to determine the number of principal singular value related to signal to noise ratio, the storage calculation of right singular matrix is performed, thus a more accurate frequency estimation of interharmonics can be obtained.

通过分析噪声误差，提出采用奇异值总体最小二乘(singular value decomposition total least squares，SVDTLS)算法进行间谐波频率估计，即同时考虑矩阵方程两边的噪声干扰，采用SVDTLS算法求解该情况下的最小范数解，通过对增广矩阵进行奇异值分解(singular value decomposition，SVD)，采用简单实用的与信噪比相关的主奇异值个数确定方法对分解的右奇异矩阵进行存储计算，得到了较精确的间谐波频率估计结果。

Analyzing the inner configuration of the covariance matrix, a new multiple targets DOA tracking algorithm is presented based on a matrix norm minimization technique.

摘要该文分析了协方差矩阵的内部结构，得到了一种具有较低运算量的基于范数最小准则的多目标DOA跟踪算法。

Firstly, we apply block AOR method to find the least square solution of minimal norm to the rank deficient linear systems where A is a complex m*n matrix with rank k.

首先，我们把求解线性方程组的块加速超松弛迭代法应用于求解亏秩线性方程组的最小范数最小二乘解，其中线性方程组的系数矩阵A是秩为k的m*n复矩阵。

Moreover, Problem I can be transformed equivalently into a problem that finding the minimum norm least-squares solution of a new inconsistent matrix equation.

而问题Ⅰ可等价转化为求一个新的不相容矩阵方程的最小范数最小二乘解的问题。

We construct a kind of special matrix function, which is used to characterize the minimization property of this iterative method, and prove that the approximate solution, generated by this iterative method, minimizes this kind of matrix function over a special affine subspace, which means that the Frobenius norm of the residual sequence is strictly monotone decreasing.

通过构造一类特殊的矩阵函数来刻画该迭代方法的极小化性质，并证明了由该迭代方法计算出来的逼近解，可使得这类矩阵函数在一个仿射子空间上达到极小，而且所得到的残差序列的Frobenius范数是严格单调递减的。

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^*。

Furthermore, its optimal approximation to a given matrix X can be obtained by finding the least-norm centrosymmetric solution of a new matrix equation AXB+CXD=F.

对任意给定的矩阵Xo，矩阵方程AXB+CXD=F的最佳逼近中心对称解可以通过迭代求解新的矩阵方程AXB+CXD=F的极小范数中心对称解而得到。

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

另外，给定中心对称矩阵对，通过求矩阵方程的中心对称解对，得到它的最佳逼近中心对称解对。

By this iterative method ,the solvability of the matrix equation can be judged automatically.When the matrix equation is consistent ,then,for any initial centrosymmetric matrix pair ,a centrosymmetric solution pair can be obtained within finite iteration steps in the absence of roundoff errors, and the least norm centrosymmetric solution pair can be obtained by choosing a special kind of initial centrosymmetric matrix pair.

当矩阵方程相容时，对任意初始的中心对称矩阵对在没有舍入误差的情况下，经过有限步迭代，得到它的一个中心对称解，并且，通过选择一种特殊的中心对称矩阵对，得到它的最小范数中心对称解。

X(k+1)\}=AX\}(1) where A is an n×n fuzzy matrix, the n-tuple fuzzy vector X(0) is a starting state, AX are products of fuzzy matrices in the sense of max-T and T is a triangular norm.

考察如下模糊离散动力系统X(k+1)=AX (1)其中A为n阶模糊方阵，系统初态X(0)为n维模糊向量，AX为max-T 意义下模糊矩阵的乘积， T为三角模。

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。