Logarithmic convergence rate of Levenberg–Marquardt method with application to an inverse potential problem
From MaRDI portal
Publication:5745462
DOI10.1515/jiip.2011.034zbMath1279.65063OpenAlexW2018750075MaRDI QIDQ5745462
Christine Böckmann, Athassawat Kammanee, Hans-Andreas Braunß\
Publication date: 30 January 2014
Published in: jiip (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/jiip.2011.034
discrepancy principleLevenberg-Marquardt methodlogarithmic source conditioninverse potential problemslogarithmic convergence rate
Fixed-point theorems (47H10) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)
Related Items
Newton Lavrentiev regularization for ill-posed operator equations in Hilbert scales ⋮ Estimation of heat flux in two-dimensional nonhomogeneous parabolic equation based on a sufficient descent Levenberg-Marquardt algorithm
Cites Work
- The regularizing Levenberg-Marquardt scheme is of optimal order
- Padé iteration method for regularization
- On a regularized Levenberg-Marquardt method for solving nonlinear inverse problems
- On the convergence of a regularizing Levenberg-Marquardt scheme for nonlinear ill-posed problems
- A regularizing Levenberg - Marquardt scheme, with applications to inverse groundwater filtration problems
- A gradient descent method for solving an inverse coefficient heat conduction problem
- Analysis of Profile Functions for General Linear Regularization Methods
- Definitions and examples of inverse and ill-posed problems
- Convergence rate analysis of the first-stage Runge–Kutta-type regularizations
- A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions
- Logarithmic convergence rates of the iteratively regularized Gauss - Newton method for an inverse potential and an inverse scattering problem
- Geometry of linear ill-posed problems in variable Hilbert scales
- Regularization of exponentially ill-posed problems
- Iterative methods for the reconstruction of an inverse potential problem
- Tikhonov regularization of nonlinear ill-posed equations under general source condition
- Iterative Runge–Kutta-type methods for nonlinear ill-posed problems
- How general are general source conditions?
