A generalization of continuous regularized Gauss–Newton method for ill-posed problems
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Abstract
A generalization of a simplified form of the continuous regularized Gauss–Newton method has been considered for obtaining stable approximate solutions for ill-posed operator equations of the form F(x) = y, where F is a nonlinear operator defined on a subset of a Hilbert space ℋ1 with values in another Hilbert space ℋ2. Convergence of the method for exact data is proved without assuming any specific source condition on the unknown solution. For the case of noisy data, order optimal error estimates based on an a posteriori as well as an a priori stopping rule are derived under a general source condition which includes the classical source conditions such as the Hölder-type and logarithmic type, and certain nonlinearity assumptions on the operator F.
© de Gruyter 2011
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Articles in the same Issue
- Logarithmic convergence rate of Levenberg–Marquardt method with application to an inverse potential problem
- Regularization and error estimate for a spherically symmetric backward heat equation
- Inverse problem and null-controllability for parabolic systems
- Determination of sets with positive reach by their projection type images
- On a finite asymptotic integral transform
- Exponential instability in the Gel'fand inverse problem on the energy intervals
- A generalization of continuous regularized Gauss–Newton method for ill-posed problems
- Direct and inverse problems of the theory of wave propagation in an elastic inhomogeneous medium
- Determination of the unknown time dependent coefficient p(t) in the parabolic equation ut = Δu + p(t)u + φ(x, t)
- Michael V. Klibanov
- International Conference “Inverse and Ill-Posed Problems of Mathematical Physics” dedicated to the 80th birthday of Academician M. M. Lavrentiev
- The Sixth International Conference “Inverse Problems: Modeling & Simulation”
- Third International Scientific Conference and Young Scientists School “Theory and Computational Methods for Inverse and Ill-Posed Problems”
