A modified algorithm for the Perron root of a nonnegative matrix with centrosymmetric structure

The matrix with centrosymmetric structure is an important kind of structured matrices with many applications in various physics and engineering problems. In this paper, we focus on the spectral radius of a subclass of centrosymmetric matrix, the nonnegative matrix with centrosymmetric structure. We discuss some results about the Perron root of a nonnegative centrosymmetric matrix. Then, the Collatz-Wielandt method for the Perron root of a nonnegative irreducible matrix is introduced, based on which a corresponding new algorithm is constructed. We show that the new algorithm ensures significant savings of computation and time cost.