Two CSCS-based iteration methods for absolute value equations with Toeplitz structure

Recently two kinds of HSS-based iteration methods to solve the absolute value equation (AVE) are proposed. In present paper, we focus on developing the CSCSbased methods for solving the absolute value equation (AVE) involving the Toeplitz structure, and propose the Picard-CSCS method and the nonlinear CSCS-like iterative method. With the help of introducing a smoothing approximate function, we give some theoretical analyses for the convergence of the CSCS-based iteration methods for AVE. The advantage of these methods is that they do not require storage of coefficient matrix, and the linear sub-systems can be solved efficiently via fast Fourier transform (FFT). Therefore, computational workloads and computer storage may be saved in actual implementations. Extensive numerical experiments are employed to demonstrate the feasibility, robustness and effectiveness of the CSCS-based methods and to compare with the recent methods.