Logarithmic convergence rates of the iteratively regularized Gauss - Newton method for an inverse potential and an inverse scattering problem
Логарифмические скорости сходимости итерационно регуляризованного метода Гаусса—Ньютона для обратной задачи о потенциале и обратной задачи рассеяния
1997-10-01
SCID: 54.1/vecbq48n
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inverse potential probleminverse scattering problemiteratively regularized Gauss–Newton methodlogarithmic convergence rateslogarithmic source condition
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Abstract (AI)
Convergence and logarithmic convergence rates of the iteratively regularized Gauss - Newton method in a Hilbert space setting are proven provided a logarithmic source condition is satisfied. This method is applied to an inverse potential and an inverse scattering problem, and the source condition is interpreted as a smoothness condition in terms of Sobolev spaces for the case where the domain is a circle. Numerical experiments yield convergence and convergence rates of the form expected by our general convergence theorem.
Key Findings
1
Convergence and logarithmic convergence rates are established for the iteratively regularized Gauss–Newton method in Hilbert spaces under a logarithmic source condition.
2
For circular domains, the logarithmic source condition is interpreted as a smoothness requirement formulated in Sobolev spaces.
3
Numerical experiments demonstrate convergence and rates consistent with those predicted by the general convergence theorem.
4
The method is applied to both an inverse potential problem and an inverse scattering problem.
Research Object
inverse potential and inverse scattering problems
Research Subject
logarithmic convergence rates of the iteratively regularized Gauss–Newton method under logarithmic source conditions
Publication Details
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1997-10-01
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