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A dynamical system method for nonlinear ill-posed equations with monotone operators
by
Li Li
Dept. of Math, Harbin Institute of Technology, Harbin, P. R. China
Coauthors: Bo Han
The goal of this paper is to investigate the dynamical system method for solving nonlinear ill-posed problems F(x)=0, where F:H→ H is a nonlinear monotone operator between Hilbert space H. Based on a lemma describing asymptotic behavior of solutions of a nonlinear integral inequality and convergence theorem in [], we apply techniques to the continuous analog of modified Landweber iteration method with monotone operator, i.e., [x\dot](t)=-F'(x(t))*F(x(t))-a(t)(x(t)-x0), and obtain the convergence theorem when noisy data d = 0 and d ≠ 0, respectively. Under certain conditions concerning the nonlinear operator F and the smoothness of the unknown solution x, stability estimates is derived, which shown that the accuracy of the continuous method is order optimal, provided that the regularization parameter has been chosen by a generalized discrepancy principle.
Date received: February 5, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavk-99.