Invariant Sets for Nonlinear Elliptic and Parabolic Systems

1980 ◽  
Vol 11 (6) ◽  
pp. 1075-1103 ◽  
Author(s):  
Hendrik J. Kuiper
2018 ◽  
Vol 52 (3) ◽  
pp. 1085-1107 ◽  
Author(s):  
Daijun Jiang ◽  
Hui Feng ◽  
Jun Zou

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.


2004 ◽  
Vol 339 (2) ◽  
pp. 145-150 ◽  
Author(s):  
José R. Galo ◽  
Isidoro I. Albarreal ◽  
M. Carmen Calzada ◽  
José Luis Cruz ◽  
Enrique Fernández-Cara ◽  
...  

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