Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations

100%

Shobha M., Argyros I., George S.

Applicationes Mathematicae

2014

tom 41

nr 1

107-129

We use a combination of modified Newton method and Tikhonov regularization to obtain a stable approximate solution for nonlinear ill-posed Hammerstein-type operator equations KF(x) = y. It is assumed that the available data is $y^{δ}$ with $||y - y^{δ}|| ≤ δ$, K: Z → Y is a bounded linear operator and F: X → Z is a nonlinear operator where X,Y,Z are Hilbert spaces. Two cases of F are considered: where $F'(x₀)^{-1}$ exists (F'(x₀) is the Fréchet derivative of F at an initial guess x₀) and where F is a monotone operator. The parameter choice using an a priori and an adaptive choice under a general source condition are of optimal order. The computational results provided confirm the reliability and effectiveness of our method.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Argyros I.

1 George S.

1 Shobha M.

1 2014

Wyniki wyszukiwania

Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations