Two Numerical Methods For Solving Absolute Value Equations

As is known to all, solving the absolute value equations Ax-|x|= b is NP-hard, where A∈Rn×n,b∈Rn are given,and |x| denotes the component wise absolute value of vector x∈Rn.This paper considers two numerical methods to solve absolute value equations Ax-|x|=b. Firstly, we consider the generalized Newton method which is proposed in [1],and prove that the generalized Newton method could find a solution for absolute value equations in finite many iterations under a weaker assumption.The numerical results indicate the efficiency of the method.Secondly, we reformulate such absolute equations into a unconstrained minimization problem,and solving the absolute value equations by unconstrained optimization algorithms.Then we prove the global convergence of the algorithms under the suitable conditions,and the experimental re-sults indicate the efficiency of the method.