The nonlinear HSS-like iteration method for absolute value equations

Two CSCS-based iteration methods for solving absolute value equations

“…Motivated by the pioneer work of [17,18], we extend the conventional CSCS iteration method to two types of CSCS-based iteration methods for solving AVEs (1.1). These methods fully exploit the Toeplitz structure to accelerate the computation speed and save storage.…”

“…Recalling that the Picard iteration method is a fixed-point iterative method and the linear term Ax and the nonlinear term |x| + b are separated [17,18], the AVEs (1.1) can be solved by using the Picard iteration method…”

“…. of the inner CSCS iteration steps are often problem-dependent and difficult to be determined in actual computations [17,18,32]. Moreover, the iterative vector can not be updated timely.…”

“…In recent years, the Picard-HSS iteration method and the nonlinear HSS-like iteration method are established to solve the AVEs in [17,18], respectively. The sufficient condition is given to guarantee the convergence of the Picard-HSS iteration method, and numerical experiments are employed to illustrate the effectiveness of the Picard-HSS and nonlinear HSS-like iteration methods.…”

“…We consider the special case of A with non-Hermitian Toeplitz structure in this paper, and a Toeplitz matrix A has the so-called circulant and skew-circulant splitting (CSCS) [22]. Inspired by the similar strategies of [17,18], two kinds of CSCS-based iteration methods are established to solve AVEs (1.1) efficiently. In the first, convergence conditions of the Picard-CSCS iteration method will be investigated.…”