| Abstract: | In this talk, we consider the solution of Hermitian positive definite Toeplitz-plus-diagonal system. Unlike the case of Toeplitz systems, no fast direct solvers have been developed for solving such system of linear equations. Hence, we employ the preconditioned conjugate gradient method with approximate inverse preconditioner to solving such system. The proposed preconditioner can be constructed and implemented efficiently by using fast Fourier transforms. We show that if the entries of the Toeplitz matrix decay exponentially away from the main diagonals, the preconditioned CG method converges very quickly. Some applications are given to illustrate the effectiveness of the proposed preconditioner. |
