对角占优矩阵

In chapter one, firstly, we introduce the properties of αdiagonally dominant matrix and some exists determination conditions of generalized strictly diagonally dominant matrix, then we give some new results for the criteria of generalized strictly diagonally dominant matrix, finally, we show the validity of these conclusions.

在第一章中，首先引述了α-对角占优矩阵的性质及已有的一些判定条件，给出了判定广义严格对角占优矩阵的几个新的结论，最后说明了这些结论的有效性。

In chapter two, by using the elements of the matrix we first construct some multiplier factors, then, use the properties of αdiagonally dominant matrix and the techniques of inequalities, we give some new determination conditions for generalized strictly diagonally dominant matrix, these theory have improved some existing results.

在第二章中，利用矩阵某些元素，构造出了几个乘积因子，然后利用α-对角占优矩阵的一些性质，结合放缩不等式的技巧，给出了广义严格对角占优矩阵的几个新的判定条件，改善了已有的某些结果。

By using the properties of part matrix elements in N1 , and by looking for positive diagonal matrix factors, we present some new sufficient conditions of generalized strictly diagonally dominant matrix and improve the recent results.

第二章在行非严格对角占优集N_1划分为N_1~(1)与N_1~(2)的直和N_1~(1)⊕N_1~(2)的条件下，利用下标在N_1上部分矩阵元素的性质，寻求正对角矩阵因子，给出了广义严格对角占优矩阵的几个新的充分条件，同时改进了近期的一些结果。

The second part is the judge method and its improvement method of a matrix is a diagonally dominant matrix: Introduces some basic methods to judge a matrix be a diagonally dominant matrix .Gives some improvement methods, and some number examples.

第二部分为广义严格对角占优矩阵的判定方法及其改进：介绍判定广义严格对角占优矩阵的一些基本方法，给出一些广义严格对角占优矩阵判定方法的改进，并给出数值例子。

If A∈Rn×n is a L-matrix,and A isn't a diagonally dominant matrix,then some properties of the quasi diagonally dominant matrix with chain of non-zero elements were given.

对角占优矩阵、拟对角占优矩阵、H-矩阵等特殊矩阵在许多工程领域中起着很重要的作用，吸引了许多数学工作者对它的性质进行研究[1-5]。

In chapter three, at first we introduces two kinds locally double αdiagonally dominant matrix from the concept of αdiagonally dominant matrix, by using this conception and the properties of αdiagonally dominant matrix and the techniques of inequalities, we discuss the relation of locally double αdiagonally dominant matrix and generalized strictly diagonally dominant matrix, according to these relations we obtain some effective criteria for generalized strictly diagonally dominant matrix.

在第三章中，首先由α-对角占优矩阵的定义，引进了两类局部双α对角占优矩阵，并利用它们及α-对角占优矩阵的性质，结合放缩不等式的技巧，讨论了局部双α对角占优矩阵与广义严格对角占优矩阵的关系，并由此得到判定广义严格对角占优矩阵的几个实用准则。

Examples illustrate that some special properties of the diagonally dominant matrix with chain of non-zero elements probably doesn't come into existence for quasi diagonally dominant matrix with chain of non-zero elements.

譬如目前关于拟对角占优矩阵的判定定理就有数十条之多[6-7]，至今仍有许多相关结论发表，其中杨志明[1]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的分布情况进行了讨论。

The third part is the judge method and its improvement method of a piece matrix is a diagonally dominant matrix: By using the Schur repair property of matrices, gives the sufficient and necessary conditions to judge a piece matrix be a diagonally dominant matrix.

第三部分为分块广义严格对角占优矩阵的判定方法及其改进：利用矩阵Schur补的性质，给出判定分块广义严格对角占优矩阵的充要条件，并利用逐次降阶的方法，使一个任意阶矩阵A逐次降为只需要利用定义判定一个矩阵是否满足要求，从而判定A是否是广义严格对角占优矩阵。

In this chapter, we show that Perron complements of N_0~2-matrices are N_0~2-matrices. We also demonstrate the Perron complements of inverse N_0~1-matrices are inverse N_0~1-matrices with certain restriction.

第四章研究非严格广义双对角占优矩阵的Schur余的性质，对角占优矩阵是数值计算中经常遇到的一类矩阵，它的Schur余可应用于迭代法的构造。

For example,,,where .2.Convergence of the iterative method: firstly I give a new upper bound for the spectral radius of iterative matrix , where is a double strictly diagonal dominant matrix.

迭代法的收敛性分析：首先给出了一般迭代阵谱半径新的上界估计，其中矩阵为双严格对角占优矩阵，是一种比严格对角占优更广泛的矩阵类。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐