An improved generalized Newton method for absolute value equations

In recent years the interest in studying the absolute value equation has been of great interest both theoretically and practically. The main reason for this is that various optimization problems, such as the complementary linear programming problem, can be written in the form of a robust equation that is easier to solve. The main purpose of this paper is to present a duplicate method for solving the equations of magnitude. Actually, in this paper, by introducing a scalar matrix, an improved generalized Newton method is proposed to solve the Absolute value equation. This new method is based on the methods of Mangserin [1] and Li [2]. In fact, if in the matrix A + αI-D, the value of the identity matrix coefficient is equal to zero, the Mangserin method and if the coefficient of the same matrix to one, the Li method is obtained. when all the singular values of the system matrix exceed one.