Two-step newton-tikhonov method for Hammerstein-type equations : finite-dimensional realization

Abstract EN

Finite-dimensional realization of a Two-Step Newton-Tikhonov method is considered for obtaining a stable approximate solution to nonlinear ill-posed Hammerstein-type operator equations KF(x)=f.

Here F:D(F)⊆X→X is nonlinear monotone operator, K:X→Y is a bounded linear operator, X is a real Hilbert space, and Y is a Hilbert space.

The error analysis for this method is done under two general source conditions, the first one involves the operator K and the second one involves the Fréchet derivative of F at an initial approximation x0 of the the solution x̂: balancing principle of Pereverzev and Schock (2005) is employed in choosing the regularization parameter and order optimal error bounds are established.

Numerical illustration is given to confirm the reliability of our approach.