Numerical methods for QBD matrix equations

In this paper, we investigate the numerical solution of QBD matrix equations. Firstly, the existence of minimal nonnegative solution for the equation is proved under a general condition. Then, a modified fixed point iteration method and a modified Newton iteration method are proposed to compute the minimal nonnegative solution, and convergence analysis of the two iteration methods is proved. Theoretical analysis and numerical experiments show that the numerical methods proposed in this paper are feasible and effective.