正定矩阵

A parallel split iteration algorithm for MIMD distributivity memory cluster on solving linear coefficient matrices is established in chapter three. Convergence is proved when the coefficient matrix is Hermite positive definite matrix or M-matrix. Discussing convergence range of parameter T . In the end, examples have been implemented on HPrx2600 cluster, and the data verify that the algorithm has favorable astringency and parallelism.

研究了一种适合于MIMD分布式存储并行机的交替方向法，理论上证明了在系数矩阵为Hermite正定矩阵和M-矩阵时算法的收敛性，讨论了参数τ的收敛范围，最后在HPrx2600集群上进行数值试验，结果表明此算法有良好的收敛性与并行性。

In this document we mainly research special matrix's decomposition, and also through the study of the theory of real reversible matrix decomposition, analysis and summarize one kind of analysis method's compact computation form of the solid invertible matrix.

本文主要研究了特殊矩阵正定矩阵的分解理论，通过对实可逆矩阵的分解理论的研究，分析总结出实可逆矩阵的一种分解方法的紧凑计算格式。

The classic iterative ones need special characters of the coefficient matrix; CG has over linear convergence, but the coefficient matrix is positive definite; Krylov subspace ones can deal with non-symmetric linear systems, but sometimes it must face"collapse"problems.

经典迭代法的收敛需要由系数矩阵的一些特定性质来保证；共轭梯度法具有超线性收敛性，但是系数矩阵必须是正定矩阵；Krvlov子空间法可用于非对称矩阵问题，但可能出现崩溃现象。

Lyapunov second method is applied to analysis of partial stability of equilibrium of linear ordinary differential equation with constant coefficients, the problems on partial stable matrix, partial positive definite matrix and Lyapunov matrix equation are studied.

将Lyapunov第二方法用于研究常系数线性系统零解的部分变元渐近稳定性，可引出相关的一些特殊矩阵问题，包括部分稳定矩阵、部分位正定矩阵、矩阵方程的可解性等。

In this paper,new quadratic PEk method and quadratic EPEk method are given for solving a system of linear algebraic equations whose matrix of coefficients is tridiagonal blocked matrix.

建立求解系数矩阵为分块三对角矩阵的线性代数方程组的新型二次PEk方法以及其外插迭代二次EPEk方法，对系数矩阵为对称正定矩阵情形，证明了新型二次PEk方法和二次EPEk方法的可解性和收敛性

Criterions of partial stable matrix and normal form of partial positive definete matrix are given, some conditions of solvability and uniqueness of Lyapunov matrix equation are discussed.

给出了部分稳定矩阵的几种判据与部分位正定矩阵的标准型，研究了矩阵方程可解性、唯一性的几种条件，提出一些可供进一步研究的问题。

Furthermore, the sufficient conditions for convergence were given when the coefficient matrix A is a Hermite positive definite matrix or Mmatrix respectively.

给出了系数矩阵分别为Hermite正定矩阵和协矩阵时算法收敛的充分条件。

Gave the concept of generalized positive definite matrices for the first time in 1970, the scholars, after 39 years' tough research, have put forward many more generalized positive definite matrix and acquired huge achievement.

首次给出广义正定矩阵的概念以来，学者们历经39年的艰苦研究历程，产生了许许多多更加广义的正定矩阵，获得许多丰富的研究成果。

In this paper, we get several properties about this kind of matrix including three adequate conditions and two contract forms according to the important properties of regular matrix and exchangeable matrix.

利用正规矩阵和乘积可交换矩阵的重要性质，给出了亚正定矩阵的三个充分条件以及其合同矩阵的两个分解形式。

Chapter 2 is devoted to the discussion of the synchronization of coupled dynamical systems with the external coupling matrices being n × n irreducible circulant real matrices having zero row sum and nonnegative off-diagonal elements and internal coupling matrices being m × m symmetric positive definite matrices.

在第二章我们讨论了耦合动力系统中，当外部耦合矩阵是n×n阶实循环不可约，行和为零且对角线以外的元素非负的矩阵，内部耦合矩阵是m×m阶对称正定矩阵时耦合系统的同步问题。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷