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By looking for positive diagonal matrix factors, we present several types of practical criteria for identifying generalized strictly diagonally dominant matrix, improve and extend some existing results.

本文利用寻找正对角矩阵因子的方法,给出了广义严格对角占优矩阵几种不同类型的实用判别法,改进和推广了一些已有结果。

Generalized strictly diagonally dominant matrix plays an important role in matrix theory and real applications.

广义严格对角占优矩阵在矩阵理论和实际应用中具有重要的作用和意义。

In this paper we present an estimate for bounds of module of eigenvalues of the iteration matrix M^(-1)N for a kind of Baily-Crabtree diagonally dominant matrix M.

该文对一类Baily-Crabtree型对角占优矩阵M,给出了迭代矩阵M^(-1)N的特征值模的上下界估计。

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。

Generalized diagonally dominant matrix、 M-matrix andH-matrix play an important role in numerical algebra、economy、cybernetics theory and so on.

对角占优矩阵、M-矩阵、H-矩阵是应用范围很广的特殊矩阵类,它们在数值代数、数量经济学、控制理论等领域都有重要作用。

Particularly, for some generalized diagonally dominant matrix M, upper bounds of the spectral radius of the iterative matrix M~(-1)Nare presented.

对矩阵M-为几类广义对角占优矩阵的情形,给出了迭代矩阵M~(-1)N谱半径的上界估计式。

In this paper,the estimates of upper bounds for the spectral radius of the iterative matrix M~(-1)N for some generalized diagonally dominant matrix M are presented.

对几类广义对角占优矩阵M,给出了迭代矩阵M~(-1)N谱半径的上界估计式,所得结果较已有结果适用于更加广泛的矩阵类。

In chapter four, by defining and studying a type of local doublediagonally dominant matrix, we give some new criteria foridentifying generalized strictly diagonally dominant matrix, andextend some existing results.

第四章定义了一种局部双对角占优矩阵,给出了广义严格对角占优矩阵的几个新判别法,推广了已有的一些结果。

In chapter three, we divide the rows of matrix into types finer than those in chapter one. Again by looking for positive diagonal matrix factors, we obtain several new criteria for identifying generalized strictly diagonally dominant matrix, improving some existing criteria.

第三章在下标集N 递进式划分的条件下,根据递进后,某些下标集上部分矩阵元素的性质,寻求正对角矩阵因子,获得了广义严格对角占优矩阵的几个新判别法,同时改进了一些已有结果。

Quasi diagonally dominant matrix with chain of non-zero elements ; Comparison matrix ; Principal minor

本文主要讨论了拟具非零元素链对角占优矩阵的几个性质,丰富了拟具非零元素链对角占优矩阵的理论。

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