DSM of Newton type for solving operator equations F(u) = f with minimal smoothness assumptions on F Online publication date: Sun, 04-Jul-2010
by N.S. Hoang, A.G. Ramm
International Journal of Computing Science and Mathematics (IJCSM), Vol. 3, No. 1/2, 2010
Abstract: This paper is a review of the authors' results on the Dynamical Systems Method (DSM) for solving operator equation (*) F(u) = f. It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F. It is assumed that F is continuously Frechet differentiable, but no smoothness assumptions on F′(u) are imposed. The DSM for solving equation (*) is developed. Under weak assumptions global existence of the solution u(t) is proved, the existence of u(∞) is established, and the relation F(u(∞)) = f is obtained. The DSM is developed for a stable solution of equation (*) when noisy data fδ are given, ''f − fδ'' ≤ δ.
Online publication date: Sun, 04-Jul-2010
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