非负矩阵Perron根的下界序列

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.本文结合非负矩阵的迹分两种情况给出Perron根的下界序列,并且给出数值例子加以说明.

非负矩阵Perron根的下界序列

为了得到非负矩阵Perron根界的估计,通过引入幂函数对Yu.A.Alpin不等式进行改进,得到一列单调递增且收敛于Perron根的下界序列,并利用非负不可约矩阵的性质,研究了一类特殊非负矩阵的下界序列。最后通过数值实例对新的估计方法进行验证,结果优于文献[3-5]中的结论。

More on Convering Squares with Squares

This paper improves some lower bounds of a function f(x) introduced in the problem of covering squares with squares.

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

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 calcu-lated 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.