【摘要】 非奇异H-矩阵在数值线性代数的理论与应用中起着重要作用,因此研究非奇异H-矩阵的判定条件有着非常重要的理论价值.本文根据广义严格α-链对角占优矩阵和广义严格α-对角占优矩阵的性质,通过引入迭代因子,给出了一组非奇异H-矩阵新的迭代判定条件.该判定条件推广和改进了相关已有结果,丰富和完善了非奇异H-矩阵的理论,最后用数值算例说明了其有效性.更多还原

【Abstract】 Nonsingular H-matrices play important roles in the theory and application of numerical linear algebra, therefore, it is very important for us to study the determinate conditions for a nonsingular H-matrix. In this paper, we present some sufficient conditions for nonsingular H-matrices according to the properties of generalized strictly α-chain diagonally dominant matrices, generalized strictly α-diagonally dominant matrices and by introducing the iteration factors. The proposed conditions improve some related results and the theory of nonsingular H-matrices is also enriched. Finally, the effectiveness of these sufficient conditions is illustrated with numerical examples.更多还原