An algorithm of diagonal transformation for Perron root of nonnegative irreducible matrices

It is always to use diagonal transformation for the estimation of nonnegative matrix’s Perron root. However, it is invalid for some matrices or a long distance of bounds generated sometimes. So the application of this method is limitation. Therefore in this paper a condition of a diagonal transformation is researched and a new method is proposed for nonnegative irreducible matrices. This method can be used for all nonnegative irreducible matrices and its’ convergence is proved in theory. It is convenient to compute by this method and it is easy to get the precision you wanted. It is proved by numerical testing that this method is valid and efficient.