کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9511194 1701082 2019 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Regula falsi based automatic regularization method for PDE constrained optimization
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Regula falsi based automatic regularization method for PDE constrained optimization
چکیده انگلیسی
Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the mismatch between the observed data and the model predictions, including an extra regularization term, and use the PDE as a constraint. Often, a suitable regularization parameter is determined by solving the problem for a whole range of parameters -e.g. using the L-curve -which is computationally very expensive. In this paper we derive two methods that simultaneously solve the inverse problem and determine a suitable value for the regularization parameter. The first one is a direct generalization of the Generalized Arnoldi Tikhonov method for linear inverse problems. The second method is a novel method based on similar ideas, but with a number of advantages for nonlinear problems.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 348, 1 March 2019, Pages 14-25
نویسندگان
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