Abstract
We prove logarithmic convergence rate of the Levenberg–Marquardt method in a Hilbert space if a logarithmic source condition is satisfied. This method is applied to an inverse potential problem. Numerical implementations demonstrate the convergence rate.
Keywords.: Levenberg–Marquardt method; inverse potential problems; logarithmic convergence rate; discrepancy principle; logarithmic source condition
Received: 2010-03-06
Published Online: 2011-08-05
Published in Print: 2011-August
© de Gruyter 2011
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- Regularization and error estimate for a spherically symmetric backward heat equation
- Inverse problem and null-controllability for parabolic systems
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- International Conference “Inverse and Ill-Posed Problems of Mathematical Physics” dedicated to the 80th birthday of Academician M. M. Lavrentiev
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Keywords for this article
Levenberg–Marquardt method;
inverse potential problems;
logarithmic convergence rate;
discrepancy principle;
logarithmic source condition
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”