Dynamical Systems Method (DSM) for general nonlinear equations
نویسنده
چکیده
If F : H → H is a map in a Hilbert space H , F ∈ C2 loc, and there exists y such that F(y) = 0, F (y) 6= 0, then equation F(u) = 0 can be solved by a DSM (dynamical systems method). This method yields also a convergent iterative method for finding y, and this method converges at the rate of a geometric series. It is not assumed that y is the only solution to F(u) = 0. A stable approximation to a solution of the equation F(u) = f is constructed by a DSM when f is unknown but fδ is known, where ‖ fδ − f ‖ ≤ δ. c © 2007 Elsevier Ltd. All rights reserved. MSC: 47H15; 47H20; 65H10; 65J15; 65N20
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تاریخ انتشار 2007