非负不可约矩阵Perron根新的下界序列

Sequences of Lower Bounds for the Perron Root of a Nonnegative Irreducible Matrix

中文关键词:  非负不可约矩阵  位移矩阵  Perron根  下界序列.

英文关键词:nonnegative irreducible matrix  shifted matrix  Perron root  lower bound.

中文摘要:

      非负矩阵Perron根的估计是非负矩阵理论研究的重要课题之一, 如果其上下界能够表示为非负矩阵元素的易于计算的函数, 那么这种估计价值更高. 本文通过构造位移矩阵给出了非负不可约矩阵Perron根的三个下界序列, 且序列是收敛到Perron根的, 最后给出数值例子与相关文献的结果进行了比较.

英文摘要:

      Estimate bounds for the Perron root of a nonnegative matrix are important in theory of nonnegative matrices. It is more practical when the bounds are expressed as an easily calculated function in elements of matrices. For the Perron root of nonnegative irreducible matrices, three sequences of lower bounds are presented by means of constructing shifted matrices, whose convergence is studied. The comparisons of the sequences with known ones are supplemented with a numerical example.