Method Of Estimation For The Greatest Eigenvalue Of The Nonnegative Matrices

In this paper,a new matrix is constructed, And a new bounds for the greatest eigenvalue of nonnegative matrices was obtained, through which the method was verified by a numerical example for higher accuracy, and the scope of this method extended to general nonnegative matrices. The structure of this paper as follows:In the first chapter, we briefly introduce the background of the greatest eigenvalue of the nonnegative matrices, the main work of this paper, we gives the definition and properties of nonnegative matrices, and some important spectrum theory of nonnegative matrix throughout the whole article. The properties of positive matrix and irreducible nonnegative matrix were introduced in detail..In the second chapter,We mainly discuss the greatest eigenvalue of positive matrix A. Through the comparison of many result about the greatest eigenvalue of the positive matrix. On the basis of previous studies, by constructing a new matrix, we give a new form to estimates the greatest eigenvalue,and the feasibility and high accuracy of the new form were proved.In the third chapter, We mainly discuss the greatest eigenvalue of nonnegative matrix A. By constructing a new matrix B= (A2-αI+A-βI)n-1, D= (A2+A+I)n-1, Where α= min{αij(2)}, β= min{αij}i, j ∈ N, We got a new form to estimate the greatest eigenvalues of the nonnegative matrices, and the feasibility and high accuracy of the new form were proved.