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Quadratic convergence of Levenberg-Marquardt method for elliptic and parabolic inverse robin problems.
- Source :
-
ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN) . 2018, Vol. 52 Issue 3, p1085-1107. 23p. - Publication Year :
- 2018
-
Abstract
- We study the Levenberg-Marquardt (L-M) method for solving the highly nonlinear and ill-posed inverse problem of identifying the Robin coefficients in elliptic and parabolic systems. The L-M method transforms the Tikhonov regularized nonlinear non-convex minimizations into convex minimizations. And the quadratic convergence of the L-M method is rigorously established for the nonlinear elliptic and parabolic inverse problems for the first time, under a simple novel adaptive strategy for selecting regularization parameters during the L-M iteration. Then the surrogate functional approach is adopted to solve the strongly ill-conditioned convex minimizations, resulting in an explicit solution of the minimisation at each L-M iteration for both the elliptic and parabolic cases. Numerical experiments are provided to demonstrate the accuracy, efficiency and quadratic convergence of the methods. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 28227840
- Volume :
- 52
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN)
- Publication Type :
- Academic Journal
- Accession number :
- 132654573
- Full Text :
- https://doi.org/10.1051/m2an/2018016