TWO CSCS-BASED ITERATION METHODS FOR SOLVING ABSOLUTE VALUE EQUATIONS

摘要

Recently, two families of HSS-based iteration methods are constructed forsolving the system of absolute value equations (AVEs), which is a class ofnon-differentiable NP-hard problems. In this study, we establish thePicard-CSCS iteration method and the nonlinear CSCS-like iteration method forAVEs involving the Toeplitz matrix. Then, we analyze the convergence of thePicard-CSCS iteration method for solving AVEs. By using the theory aboutnonsmooth analysis, we particularly prove the convergence of the nonlinearCSCS-like iterationsolver for AVEs. The advantage of these methods is that theydo not require the storage of coefficient matrices at all, and the sub-systemof linear equations can be solved efficiently via the fast Fourier transforms(FFTs). Therefore, computational cost and storage can be saved in practicalimplementations. Numerical examples including numerical solutions of nonlinearfractional diffusion equations are reported to show the effectiveness of theproposed methods in comparison with some existing methods.