对角矩阵

再根据系统的传递函数矩阵，采用PID对角矩阵解耦控制算法结合约束条件实现其解耦控制。

Then the PID diagonal matrix decoupling control algorithm was adopted in the system based on the matrix transfer function .

当A是一个M-矩阵，该算法可以得出一个相应的正对角矩阵D使得AD成为等对角优势矩阵。

When A is a M-matrix , this algorithm determines a positive diagonal matrix D so that AD is a so-called equi-diagonally dominant matrix .

不可约对称三对角矩阵特征值的Newton迭代算法

Newton Iterative Arithmetic of a Unreduced Symmetric Tridiagonal Matrix with Eigenvalues

由块三对角矩阵的LU分解，得到了其逆矩阵块元素的显式表达式。

With the LU decomposition of the block tridiagonal matrix , an explicit expression of the block inverse elements is obtained .

对称三对角矩阵的两个FORTRAN程序

Two Fortran Subroutines for Symmetric Tridiagonal Matrix

对称三对角矩阵与周期Jacobi矩阵的广义逆

The symmetric tridiagonal matrices and the generalized inverse of periodic Jacobi matrix

关于Hermite三对角矩阵的积和式

On the permanent of Hermite triple diagonal matrix

并由此给出了次U矩阵和次H矩阵化成次对角矩阵的可行性理论基础及次对角化的方法。

Fron the formula , presents tile secondary U matrix and secondary H matrix turn to the feasible theoretical basis of secondary diagonal matrix and the secondary diagonalization method .

由于正交应力模式使H矩阵成为对角矩阵，因此可以完全避免繁杂的H矩阵求逆运算，从而从根本上改进了部分杂交元方法的计算效率。

Orthogonalized stress modes make matrix H diagonal , so that multifarious calculation of solving H - 1 is avoided . Thus the computational efficiency of partial hybrid finite element is improved .

我们记其中，A，B是n×n的三对角矩阵，我们建立了下面的定理定理1：对任何固定，假如，其中Si是下面方程的解。

Thus we write : where A , B are the tri-diagonal matrices of n × n , given by Hence the following theorems are established : theorem 1 . for any fixed ;

对称三对角矩阵QL算法的一种新位移

A new shift of the QL algorithm for the symmetric tridiagonal matrices

对称三对角矩阵QL算法的按序收敛

On convergence of eigenvalues in natural order for symmetric tridiagonal QL algorithm

基于半导体图像传感器CCD的物理图像和相应的基本特性微分方程组，经过离散和线性化处理，并引用解三对角矩阵方程的递归算法，实现了其解析模型求解。

In the light of CCD 's physical image and its basic differential equations , an analytical model is developed , which is processed by dispersed and linearized methods .

本文在原三对角矩阵BP算法的基础上推出了一种新的原油蒸馏过程计算方法，并探讨了过程的产品质量估计和优化管理问题。

A New calculation method based on the original tridiagonal BP method is developed for solving problems of crude distillation process . The problems of product quality estimation and supervision are particularly studied .

不可约实对称三对角矩阵QL算法的RWε位移

The rw ε shift of the QL algorithm for irreducible real symmetric tridiagonal matrices

最重要的是用两种不同的方法研究了带有比例关系的实五对角矩阵特征值反问题，讨论了问题B1和问题B2有唯一解的条件，给出解的表达式，并分别给出数值例子验算。

The most important thing is to use two different methods to study inverse eigenvalue problem for real five-diagonal matrices with proportional relation .

对角矩阵及三角矩阵之特征值，相似矩阵，由QR分解计算特征值，主特征值之迭代估算。

Eigenvalues of diagonal and triangular matrices , similarity transforms , calculation of eigenvalues from QR decomposition , iteratively estimating the leading eigenvalue .

利用有限域上的2级准对角矩阵构作Cartesian认证码，计算出了该类认证码的参数。

A construction of Cartesian Authentication Codes from 2 by 2 Quasi diagonal matrices over finite fields are presented and their size parameters are computed .

讨论了除环上无限方阵的对角化问题，证明了除环上行列有限方阵等价于一类特殊对角矩阵Dn的两个等价条件。

The diagonalization problem of infinite matrix on a division ring is discussed . The two equivalence conditions for row-column-finite-matrix A - Dn on a division ring are proved .

设G为n阶简单连通图，若Q（G）为图G的对角矩阵与邻接矩阵的和，称Q（G）为G的拟-Laplacian矩阵。

Let G be a simple connected graph with n vertices . The matrix Q ( G ) is called the quasi-Laplacian matrix of G , if it is the sum of the diagonal matrix and the adjacency matrix of G.

本软件采用三对角矩阵法求解精馏过程的MESH方程组，用VISUALBASIC6.0开发出缔合体系精馏模拟软件，同时软件也包括了一般体系的多元复杂精馏模拟。

The MESH equations were solved by trigonometric matrix in distillation simulation process . The software for simulating distillation process of association system was programmed using Visual Basic 6.0.The software can be also used to simulate distillation process of general systems .

分别基于块三对角矩阵的绞形分解、块LU分解和基于用四个分块的列向量表示块逆矩阵三种方法进行了研究，得到三个简单算法。

The investigation is based on three methods : the twisted factorization 、 LU factorization of tridiagonal matrix and expression the block inverse matrix with four block column vectors . And then three simple algorithms are derived .

本文一改传统方法，从矩阵分解入手，逐步推导出一种新颖的判定方法，并给出将n阶实对称矩阵A分解为特殊三角矩阵与对角矩阵乘积的具体计算公式。

By changing the traditional method and starting with the matrix decomposition , we have made out a new method of judgment step by step and a concrete computing formula of decomposing the n real symmetric matrix A into special triangle matrix and diagonal matrix .

提供两个高效而实用的FORTRAN程序（例行子程序形式），用于对称三对角矩阵的两个计算问题（其一是线性代数方程组的求解，其二是广义特征值问题的计算）。

This paper provides two FORTRAN subroutines for the two computational problems of the symmetric tridiagonal matrix ( solution of the system of liner algebraic equations , and computation of the generalized eigenvalues and eigenvectors ) .

证明了具有与Lanczos算法结果同样形式的三对角矩阵及其相关矩阵的确定条件，同时给出了相应的定理。

Through mathematic analysis and operations , the conditions for determining the tridiagonal matrix and its relative matrices with the same form as obtained by Lanczos algorithm are proved , some theorems are established .

在轴向与径向用三对角矩阵法（TDMA），在周向采用循环三对角矩阵法（CTDMA），采用交替方向亚松弛叠代法（ADI）求解方程；

Algebraic equations are solved by iteration with a line-by-line method that is a combination of TDMA in axial and radial directions , CTDMA in tangential direction and ADI method in three directions .

本文利用Hessenberg矩阵特征值配置的一个结果以及三对角矩阵的有关性质，提出了一个求解Jacobi矩阵特征值反问题的数值方法。

A numerical method based on the eigenvalue assignment in an upper Hessenberg matrix and properties of tridiagonal matrices to solve a kind of inverse eigenvalue problems for Jacobi matrices in presented .

文中对双边投影引理和Finsler引理进行了扩展，从而可以处理基本矩阵不等式中块对角矩阵的消去问题。

A theo - rem was derived as a natural extension of two - sided projection lemma and Finsler Lemma which makes it possible to eliminate the diagonal block matrix in the basic matrix inequality .

此时，引入一个可变全局步长参数的对角矩阵，通过使后验误差向量等于干扰信号向量，推导出了适用于PAPA的可变步长方法。

In this case , it is necessary to introduce a diagonal variable step-size matrix . By forcing the the a posterior error vector to be the disturbance signal vector , after the similar process , a variable step-size method is achieved for PAPA .

应用改进的三对角矩阵法和UNIFAC模型，对粗甲醇预蒸馏塔进行了模拟计算，并对粗甲醇加水量、塔板数、回流比和进料位置等进行了分析和讨论。

The crude methanol pre-fractionator is calculated by the application of improved opposite triangle matrix technique and UNIFAC model , and crude methanol water addition , number of trays , reflux ratio and feed inlet location etc are analyzed .