A generalization of the Gauss–Seidel iteration method for solving absolute value equations

The proximal methods for solving absolute value equation

“…Cruz et al [1] used the inexact non-smooth Newton method, and established global linear convergence of the method. Salkuyeh [22] considered the PicardHSS iteration method and provided sufficient conditions for the convergence of this method, and Edalatpour et al [4] presented a generalization of the GaussSeidel iteration method for solving AVE (1). Finally, Moosaei et al [15] introduced two methods for solving AVE (1), i.e., the Homotopy perturbation method, and the Newton method with the Armijo step.…”

A Two-Step Newton-Type Method for Solving System of Absolute Value Equations

“…where A ∈ R n×n and b ∈ R n are known vectors and |x| denotes the absolute values of the components of x ∈ R n . e system of absolute value equations arises in optimization, the economies with institutional restrictions upon prices, the free boundary problems for journal bearing lubrication, and the network equilibrium problems, for example, see [1][2][3][4][5][6][7][8][9][10][11][12]. Mansoori and Erfanian [13] suggested a dynamic model to obtain the exact solution of equation (1).…”

“…e system of absolute value equations arises in optimization, the economies with institutional restrictions upon prices, the free boundary problems for journal bearing lubrication, and the network equilibrium problems, for example, see [1][2][3][4][5][6][7][8][9][10][11][12]. Mansoori and Erfanian [13] suggested a dynamic model to obtain the exact solution of equation (1). e development of multistep methods has gained popularity in the field of computational mathematics.…”

The Picard-HSS-SOR iteration method for absolute value equations

“…In recent years, the problem of finding solution of AVE has been attracted much attention and has been studied in the literature [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. For the numerical solution of the AVE (1.1), there exist many efficient numerical methods, such as the SOR-like iteration method [12], the relaxed nonlinear PHSS-like iteration method [15], the Levenberg-Marquardt method [16], the generalized Newton method [17], the Gauss-Seidel iteration method [19] and so on.…”