A dimension expanded Newton-type method for absolute value equations

By expanding the dimension of the absolute value equations, we construct two almost equivalent augmented quadratic polynomial systems, for which the singularity of the Jacobian matrices at exact solution of the original systems are analyzed. Later, by employing the conventional Newton method to the new systems, we study the numerical solution of the absolute value equations. Theoretical results and numerical examples show that our method is efficient independent of \(||A^{-1}||\) $||A^{-1}||$ .