Asymptotic properties of a stochastic predator-prey model with Crowley-Martin functional response

A two-step iterative scheme based on the multiplicative splitting iteration is presented for PageRank computation. The new algorithm is applied to the linear system formulation of the problem. Our method is essentially a two-parameter iteration which can extend the possibility to optimize the iterative process. Theoretical analyses show that the iterative sequence produced by our method is convergent to the unique solution of the linear system, i.e., PageRank vector. An exact parameter region of convergence for the method is strictly proved. In each iteration, the proposed method requires solving two linear sub-systems with the splitting of the coefficient matrix of the problem. We consider using inner iterations to compute approximate solutions of these linear sub-systems. Numerical examples are presented to illustrate the efficiency of the new algorithm.