The research for diagonally dominant matrix is the important task of matrix theory.
矩阵的对角占优性质的研究是矩阵理论中的重要课题之一。
However, from the point of view of multi-variable control theory, that arrangement is inherently infective, as when multiple SISO controllers are assigned to a MIMO (Multi-input Multi-output) system, stability of closed-loop system cannot be ensured if the transfer function matrix of the system is not diagonally dominant.
因为多变量控制理论的研究结果早已证明，这种将MIMO系统当作SISO系统的控制设计方案，在各个控制之间的交互影响不可忽略(系统传递函数矩阵不对角占优)时，即使每个控制器都能成功地单独设计，也不能保证闭环全系统的稳定性。
At the beginning of this paper, we briefly introduced the fundamental knowledge of the Newton iterative methods, and the local convergence theorem which extended the classical Newton method, because of the local convergence, the theorem had its certain restrict. Large-scale convergence theorem was proved under the condition that matrix M is irreducible diagonally dominant by Newton's method with line search. At the last part of this paper, we present the method for solving linear complementarity problems arising from journal bearings.
本文首先介绍了Newton型迭代法的基础知识，然后着重介绍了B-可微方程的Newton法，给出B-可微法的局部收敛结论，推广了古典的Newton法，但由于收敛的局部性，该算法仍有一定的不足之处；文章在证明大范围收敛定理时，假设M是不可约对角优势矩阵，采用一维Newton寻查的方法，保证算法的收敛性。
It takes full advantage of both the diagonally dominant property of the nodal admittance matrix and the symmetric property of sparseness structure.
该算法既利用了节点导纳矩阵的对角优势，又充分利用了稀疏结构的对称性。
Based on the system balanced block triangle decomposition, a coefficient matrix of system state equations can be of block diagonally dominant by using imbalanced compensating scheme; and therefore, the result of system model simplifications is ideal.
因此，在系统平衡块三角分解的基础上，利用非平衡补偿方法使系统状态方程的系数矩阵具有块对角优型，使系统模型简化的结果更为理想。
We also analyze the relative features of perron complement, H-matrix, diagonally dominant matrix, and generalized double diagonally dominant matrix.
并进一步研究了非负矩阵Perron余的有关性质，如对角占优矩阵及H矩阵的Perron余的对角占优性，以及广义双对优矩阵的Perron余的有关性质等。
In this paper the necessary and sufficient (NS) condition of real square matrix (RSM) to be a generalized strictly diagonally dominant matrix and the NS condition of the RSM's comparison matrix to be a nonsingular M-matrix are given.
文章给出了实方阵为广义严格对角占优矩阵和实方阵的比较矩阵为非奇M矩阵的充要条件。
Then we get a set of linear equations, whose coefficient matrix is sparse and diagonally dominant.
这样得到一个线性方程组，并且系数矩阵是对角占优稀疏矩阵，给计算带来了极大的方便。
Convergence Criteria of Jacobi, Gauss-Seidel, and SOR Iteration Methods in Weak Diagonally Dominant Matrix
弱对角占优矩阵的Jacobi和Gauss-Seidel及SOR迭代法收敛准则
It extends especially the condition of unreduced weak diagonally dominant matrix for the convergence of Jacobi, Gauss-Seidel, and SOR iteration methods.
特别是放宽了Jacobi，Gauss-Seidel和SOR迭代法收敛的不可约弱对角占优矩阵这一条件。
Two sufficient conditions of the existence of stable equilibrium points of nonsymmetric cellular neural networks (CNNC for short) are obtained by using the characteristics of saturation region and the relationship between quasi-diagonally column dominant and M-matrix.
利用饱和域的特性，和拟对角列支配矩阵与M-矩阵之间的关系，获得了非对称细胞神经网络（简称CNNS）的稳定平衡点存在的两个充分条件；
This paper presents a new mathematical concept: when the principal submatrix A_ (11) of A is diagonally dominant, A is calledquasi & diagonally dominant matrix.
本文提出一个数学上的新概念：矩阵A的主子块A（11）是对角线占优的，则称A是拟对角线占优矩阵。
A necessary and sufficient condition for matrix A to be generalized diagonally dominant matrix is presented.
提出局部次对角占优矩阵的概念，得到了广义次对角占优矩阵的二个充分条件。
The calculation methods of diagonally dominant matrix in-situ replacement are researched, including the matrix determinant, the matrix equation unknown and the matrix inversion computation.
研究对角占优矩阵原位替换解算方法，包括矩阵行列式、矩阵方程未知数和矩阵逆阵的解算。
The Upper Bounds for the Module of Eigenvalue of Iteration Matrix Based on Double α Diagonally Dominant Matrix
基于双α对角占优矩阵的迭代法的迭代矩阵特征值模的上界四元数体上自共轭矩阵广义酉对角化
The Fan product of two inverse M-matrices were studied, the conclusion is that if the two inverse M-matrices are both strictly diagonally dominant matrices, then the Fan product of them is M-matrix. Therefore, inequalities on the Schur complement of the Fan product were obtained.
通过研究两个逆M-矩阵的Fan积，得到当两个逆M-矩阵均为严格对角占优矩阵时，它们的Fan积为M-矩阵，进而得到有关该Fan积的Schur补不等式。
This paper defines a new class of matrix: quasi diagonally dominant matrix with chain of non-zero elements and discusses its range of eigenvalue.
给出了拟具非零元素链对角占优矩阵的定义，并就这类矩阵的特征值分布性质进行了讨论。
The estimation on the inverse elements of strictly diagonally dominant tridiagonal matrix is established; in this estimation, the nonnegative condition of matrix elements is moved.
利用严格对角占优和三对角矩阵的某些特性，推导出严格对角占优三对角矩阵逆元素的统一估计式。
Generalized strictly diagonally dominant matrix play an important role in numerical algebra、control theory、electric system、economic mathematics and elastic dynamics and so on.
广义严格对角占优矩阵具有很广的实际背景，这类特殊矩阵在数值代数、控制论、电力系统理论、经济数学及弹性力学等众多领域中有着重要的实用价值。
An equalization algorithm based on the elementary matrix transformation is proposed for the MIMO communication channel, and the corresponding blind equalization algorithm is obtained for the row-diagonally-dominant MIMO system.
对MIMO通信信道提出了一种基于矩阵初等变换的均衡算法，将其用于行对角占优的MIMO系统，则得到相应的MIMO盲均衡算法。