Abstract
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.
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