摘要：The goal of this paper is to solve the complexsymmetric linear systems generated from the discretizationof the space fractional coupled nonlinear Schrödinger (CNLS)equations, whose coefficient matrix is equal to the sum of asymmetric positive definite Toeplitz matrix and a Hermitianpositive definite complex diagonal matrix. In order to make thebest use of the full Toeplitz structure of the coefficient matrix,a new Toeplitz and diagonal splitting (TDS) is given and thecorresponding TDS iteration method is proposed to solve thediscretized linear systems, then two circulant preconditionersbased on Strang’s and T. Chan’s circulant approximation, areproposed to accelerate the convergence of the preconditionedconjugated gradient (PCG) method for solving the first linearsub-system in the TDS method. Theoretical analysis andnumerical experiments demonstrate that the TDS methodis unconditional convergence and the TDS-PCG inner-outeriteration method with two circulant preconditioners to solvethe discretization linear systems of the space fractional CNLSequations is feasible and efficient.
