Studying a numerical stable and quadratic convergence method for solving a new class of absolute value equations.

In this paper, a new class of absolute value equations is studied as follows:Ax-B|x|-b=o, ( B≠I, σ_"max" (|B|)<σ_"min" (A) ), This new class of absolute value equations, the single value absolute matrix B is less than the single value matrix A and the matrix B is not exclusively the identity matrix..Therfore the power of choice is wider than other methods of the absolute value equations and all matrices are arbitrary and this new class of absolute value equation is the NP hard problem..We solve this new class using a generalized Newton method and also convergence and numerical stability. Also, by testing the numerical examples of the efficiency and effectiveness of the solution method for the new class, it has been studied with other works that have been done including Lotfi and Zainali and Mangasarain and Khaksars method.Eceptthis new class and Lotfi and Zainali method are quadratic convergence, the rest methods are linear convergence.