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

• Autorzy: Monnanda Erappa Shobha , Ioannis K. Argyros , Santhosh George
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 65N20: Ill-posed problems
• 47A52: Ill-posed problems, regularization
• 65J20: Improperly posed problems; regularization
• 47J06: Nonlinear ill-posed problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2014
• Tom: 41
• Numer: 1
• Strony: 107-129

Daty

wydano

2014

Twórcy

autor

Monnanda Erappa Shobha

• Department of Mathematical and Computational Sciences, National Institute of Technology, Karnataka, India 757 025

autor

Ioannis K. Argyros

• Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, U.S.A.

autor

Santhosh George

• Department of Mathematical and Computational Sciences, National Institute of Technology, Karnataka, India 757 025

Identyfikatory

DOI

10.4064/am41-1-9