【作者】 杨鹏；

【导师】 黄廷祝；

【作者基本信息】 电子科技大学 ， 计算数学， 2003， 硕士

【摘要】 本文主要分两大部分:1.(块)H矩阵类的判别条件:主要是给出了(块)H矩阵的充分条件,这些条件是已有结果的推广和改进。如研究了非奇异块H-矩阵的判据,给出了两个充分条件,如对于任何,有,存在,则A为非奇块H矩阵。2.块H矩阵的充分条件的应用:在块H矩阵判定的基础上,推广其应用,给出了块H矩阵与稳定阵和亚正定的判定,接着将结果应用与与最小奇异值的估计,最后讨论了块迭代法的收敛性。更多还原

【Abstract】 This paper mainly includes two parts:1. Simple Criteria for (block)H-Matrices: we present sufficient conditions, which generalize and improve the previous results.For example:We present two sufficient conditions for H-matrix. For example,. There is an and , ,则A is a nonsingular block H-matrices.2. Applications about sufficient conditions of block H-Matrices: We spread the application base upon Simple Criteria for block H-Matrices. And we present Simple Criteria of positive stability and sub-positive definity for a block H-Matrices. The next we study the upper bounds for and the lower bounds for the smallest singular value. At last we discuss convergence of block iterative method.更多还原