On finite termination of the generalized Newton method for solving absolute value equations

Motivated by the framework constructed by Brugnano and Casulli (SIAM J. Sci. Comput. 30: 463–472, 2008), we analyze the finite termination property of the generalized Netwon method (GNM) for solving the absolute value equation (AVE). More precisely, for some special matrices, GNM is terminated in at most 2n + 2 iterations. A new result for the unique solvability and unsolvability of the AVE is obtained. Numerical experiments are given to demonstrate the theoretical analysis.