摘要
首先给出了不可约非负矩阵最大特征值的上下界。然后利用相似变换构造了一列相似矩阵,从而得到不可约非负矩阵最大特征值的逐步压缩的一列上下界,其极限为所要求的最大特征值。最后利用Z-矩阵与非负矩阵的关系,给出了计算不可约Z-矩阵最小特征值的一个新算法。理论上给出了收敛性证明。该算法迭代过程简单,不用计算逆矩阵,从而计算量小,占用内存少。数值实验的结果表明该算法具有可行性和有效性。
It is well-known that the problem to calculate the minimal eigenvalue of a matrix commonly occurs in many branches of science and engineering. In this paper, we consider the problem to calculate the minimal eigenvalue of a so-called Z-matrix. An upper and a lower bounds on the maximal eigenvalue of a nonnegative matrix are firstly given. Then by using a similarity transformation, a series of upper and lower bounds on the maximal eigenvalue of a nonnegative matrix are obtained, these bounds gradually approach the maximal eigenvalue. Finally, based on the relation between the Z-matrix and the nonnegative matrix, a numerical algorithm for computing the minimal eigenvalue of an irreducible Z-matrix is proposed. It is shown by numerical examples that the convergency rate of the presented method is faster than that of previous methods.
出处
《工程数学学报》
CSCD
北大核心
2010年第1期105-110,共6页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(10962001)
广西研究生教育创新基金(2008106080701M369)~~
关键词
非负矩阵
Z-矩阵
不可约
最小特征值
收敛率
nonnegative matrices
Z-matrices
irreducible
minimal eigenvalue
convergency rate
作者简介
刘利斌（1982年8月生），男，硕士．研究方向：数值代数
