Optimal Parameters for 2-cyclic AOR

Assume A∈Cn×nA∈Cn×n is a 2-cyclic consistently ordered matrix and J   is denoted as its associated block Jacobi iteration matrix. We consider the 2-cyclic AOR method for solving the consistent linear systems Ax=bAx=b. In the case that σ(J2)σ(J2) is either nonnegative or nonpositive, we give detailed discussion and derive definite expressions on optimal parameters and spectral radius by efficient method. Moreover, we give some numerical examples.