Estimating The Bounds And Algorithm For The Maximum Eigenvalue Of The Nonnegative Matrix

The spectral theory of nonnegative matrix is widely used in the areas of Management Science and Mathematics Economics. This paper investigates the estimating the bounds and algorithm for the maximum eigenvalue of nonnegative matrix on the basis of some spectral theories. The main contents are as follows:1,The basic knowledge of some special nonnegative matrices are introduced simply, and the relevant spectral theories are summarized.2,The bounds for the maximum eigenvalue of the nonnegative matrix are studied and some good bounds are considered especially. A new bound of the maximum eigenvalue are obtained, which is proved to be more accurate.3,A iterate method of finding the maximum eigenvalue of irreducible nonnegative matrix is presented, and the convergence theorem and error estimating of this algorithm are proved. At last, two examples are given to show that the new method is effective.