A Simple Method For Estimating The Bounds Of Spectral Radius Of Nonnegative Irreducible Matrices
Zhi Ming Yang · 2011
Based on the Perron complement P(A=A[�]) and generalized Perron complement Pt(A=A[�]) of a nonnegative irreducible matrix A, we derive a simple and practical method that estimates the upper and lower bounds of the spectral radius of A in terms of norms of A[�] and its complements. Numerical examples show that this approach improves some of the classical estimates. The spectral theory of nonnegative matrix has a wide range of applications to Operations Research, Quantitative Economics, Graph theory and Markov chain theory. In 1989, in connection with a divide and conquer algorithm for computing the stationary