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The piecewise linear system is a nonsmooth but semismooth equation. In this paper, a damped semismooth Newton method is presented for solving a class of piecewise linear systems. Under appropriate conditions, both monotone convergence and finite termination properties are investigated for the proposed method.
Semismooth Newton method is an effective method for solving a nonsmooth equation, which arises from a reformulation of the complementarity problem. Under appropriate conditions, we verify the monotone convergence of the method. We also present semismooth Newton Schwarz iterative methods for the nonsmooth equation. Under suitable conditions, the methods exhibit monotone and superlinear convergence...
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