The Limited Method Of Estimating The Spectrum Radius Of The Nonnegative Irreducible Matrices

As an elementary instrument,the theory of nonnegative matrices is widely used in numerical analysis,graph theory,computer science,management science and so on. The new bounds of the spectrum radius of the nonnegative irreducible matrices is the main problem.Those main algorithms of the spectrum radius of the nonnegative irreducible ma-trices include diagonal transformation method,Perron complementary method,iterative method and so on.If the bounds can get by elements of the nonnegative irreducible matrices and have simple calculate function,the higher value will be achieved.Based on some existing results and Collatz-Wielandt function,this article get the new bounds for the spectrum radius of the nonnegative irreducible matrices as follows: If A=(aij)n×n is the nonnegative irreducible matrices,Bm= (Am+Am-1+...+A+ have:Further,this article discuss a limited methed of estimating radius of the nonnegative irreducible matrices,the main result as follows:Both of the two conclusions are proved,the estimation of ρ(A) get higher accuracy than existing formula and numerical examples are proposed to illustrate it.Especially,the new estimated form of ρ(A) have some theoretical value.