Newton Lavrentiev regularization for ill-posed operator equations in Hilbert scalese

作者：George Santhosh; Pareth Suresan^*; Kunhanandan M

来源：Applied Mathematics and Computation, 2013, 219(24): 11191-11197.

DOI：10.1016/j.amc.2013.05.021

• Hilbert scales
• Newton method
• Lavrentiev regularization
• Monotone operator
• III-posed problems
• Adaptive method

In this paper we consider the two step method for approximately solving the ill-posed operator equation F(x) = f, where F : D(F) subset of X -> X, is a nonlinear monotone operator defined on a real Hilbert space X, in the setting of Hilbert scales. We derive the error estimates by selecting the regularization parameter alpha according to the adaptive method considered by Pereverzev and Schock in (2005), when the available data is f(delta) with parallel to f - f(delta)parallel to <= delta. The error estimate obtained in the setting of Hilbert scales {X-r}(r is an element of R) generated by a densely defined, linear, unbounded, strictly positive self adjoint operator L : D(L) subset of X -> X is optimal order.

• 出版日期2013-8-15