A study of frozen iteratively regularized Gauss–Newton algorithm for nonlinear ill-posed problems under generalized normal solvability condition
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Abstract
A parameter identification inverse problem in the form of nonlinear least squares is considered. In the lack of stability, the frozen iteratively regularized Gauss–Newton (FIRGN) algorithm is proposed and its convergence is justified under what we call a generalized normal solvability condition. The penalty term is constructed based on a semi-norm generated by a linear operator yielding a greater flexibility in the use of qualitative and quantitative a priori information available for each particular model. Unlike previously known theoretical results on the FIRGN method, our convergence analysis does not rely on any nonlinearity conditions and it is applicable to a large class of nonlinear operators. In our study, we leverage the nature of ill-posedness in order to establish convergence in the noise-free case. For noise contaminated data, we show that, at least theoretically, the process does not require a stopping rule and is no longer semi-convergent. Numerical simulations for a parameter estimation problem in epidemiology illustrate the efficiency of the algorithm.
Funding source: National Science Foundation
Award Identifier / Grant number: 1818886
Funding statement: Alexandra Smirnova is supported by NSF Grant 1818886. DMS Computational Mathematics.
References
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- A study of frozen iteratively regularized Gauss–Newton algorithm for nonlinear ill-posed problems under generalized normal solvability condition
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Articles in the same Issue
- Frontmatter
- Image reconstruction method for exterior circular cone-beam CT based on weighted directional total variation in cylindrical coordinates
- Full reconstruction of a vector field from restricted Doppler and first integral moment transforms in ℝn
- Lipschitz stability for a semi-linear inverse stochastic transport problem
- Inverse problem for elastic body with thin elastic inclusion
- Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source
- Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions
- A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification
- A linear regularization method for a parameter identification problem in heat equation
- A study of frozen iteratively regularized Gauss–Newton algorithm for nonlinear ill-posed problems under generalized normal solvability condition
- Numerics of acoustical 2D tomography based on the conservation laws
- Identification of the diffusion coefficient in a time fractional diffusion equation
- Linear least squares method in nonlinear parametric inverse problems
