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Applicationes Mathematicae

2014 | 41 | 1 | 107-129
Tytuł artykułu

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

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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.
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107-129
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wydano
2014
Twórcy
• Department of Mathematical and Computational Sciences, National Institute of Technology, Karnataka, India 757 025
autor
• Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, U.S.A.
autor
• Department of Mathematical and Computational Sciences, National Institute of Technology, Karnataka, India 757 025
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