A modified algorithm for the Perron root of a nonnegative matrix

An algorithm of diagonal transformation for the Perron root of nonnegative matrices is proposed by Duan and Zhang [F. Duan, K. Zhang, An algorithm of diagonal transformation for Perron root of nonnegative irreducible matrices, Appl. Math. Comput. 175 (2006) 762–772]. This method can be used for all nonnegative irreducible matrices. In this paper, an improved algorithm which is based on this method is proposed. The new algorithm inherits all the above-mentioned advantages of the original algorithm and has higher efficiency. It is testified by numerical testing that the efficiency of the new algorithm is improved greatly.