paper

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

arXiv:2207.04492 · doi:10.1007/s40314-023-02318-6

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 $2 n + 2$ iterations. A new result for the unique solvability and unsolvability of the AVE is obtained. Numerical experiments are given to demonstrate the theoretical analysis.

11 pages