Fast solution of general nonlinear fixed point problems
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In this paper, we develope a general procedure to stabilize the usual Newton method in such a way that algorithms obtained always converge to the unique solution of the problem.
We show that in the case where the operator T∈C1∩H2,∞, quadratic convergence holds and when T is polyhedric, convergence in a finite number of steps is obtained. Numerical results are shown for an example issued from the field of differential games.
KeywordsVariational Inequality Optimal Control Problem Differential Game Descent Direction Quadratic Convergence
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