On the SOR-like iteration method for solving absolute value equations

Iterative schemes induced by block splittings for solving absolute value equations

“…In [7], the SOR-like method is extended for solving (1). More precisely, the following iterative scheme is developed…”

“…In this section, we report some numerical results to compare the performance of proposed method with iterative schemes (2), ( 3), ( 4), ( 5) and (7). All computations were carried out on a computer with an Intel Core i7-4770K CPU @ 3.50GHz processor and 24GB RAM using MATLAB R2018b.…”

“…The matrix A in Example 3.3 is a special case of B in Example 3.1. Indeed, in [7,9] a reformulation of the matrix B is used for which r = 0. Our goals for presenting this test problem are working with larger dimensions than those examined in the first example and presenting comparison results between BBS-type iterative methods.…”

“…6 are reported to illustrate the behavior of SOR-like method in comparison with iterative scheme (10). To this end, we only work with the dimensions used in [7,Example 2] and the right-hand side b is constructed such that x * = (−1, 1, −1, 1, . .…”

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

“…The importance of the AVE (1.1) arises from the fact that linear programs, bimatrix games and other important problems in optimization all can be reduced to the system of 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.…”