Optimal convergence rates for inexact Newton regularization with CG as inner iteration

2020 ◽  
Vol 28 (1) ◽  
pp. 145-153 ◽  
Author(s):  
Andreas Neubauer
Keyword(s):  
Parameter Identification ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Regularization Method ◽  
Convergence Rates ◽  
Identification Problem ◽  
Discrepancy Principle ◽  
Parameter Identification Problem ◽  
Optimal Convergence Rates ◽  
Inner Iteration

AbstractIn this paper we prove order optimality of an inexact Newton regularization method, where the linearized equations are solved approximately using the conjugate gradient method. The outer and inner iterations are stopped via the discrepancy principle. We show that the conditions needed for convergence rates are satisfied for a certain parameter identification problem.

A linear regularization method for a parameter identification problem in heat equation

2020 ◽  
Vol 28 (2) ◽  
pp. 251-273
Author(s):  
Subhankar Mondal ◽  
M. Thamban Nair
Keyword(s):  
Heat Equation ◽  
Parameter Identification ◽  
Regularization Method ◽  
Identification Problem ◽  
Practical Application ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Choice Strategy ◽  
Parameter Identification Problem ◽  
Parameter Choice Strategy

AbstractRecently, Nair and Roy (2017) considered a linear regularization method for a parameter identification problem in an elliptic PDE. In this paper, we consider similar procedure for identifying the diffusion coefficient in the heat equation, modifying the Sobolev spaces involved appropriately. We derive error estimates under appropriate conditions and also consider the finite-dimensional realization of the method, which is essential for practical application. In the analysis of finite-dimensional realization, we give a procedure to obtain finite-dimensional subspaces of an infinite-dimensional Hilbert space {L^{2}(0,T;H^{1}(\Omega))} by doing double discretization, that is, discretization corresponding to both the space and time domain. Also, we analyze the parameter choice strategy and obtain an a posteriori parameter which is order optimal.

scholarly journals Multilayer method for solving a problem of metals rupture under creep conditions

2019 ◽  
Vol 23 (Suppl. 2) ◽  
pp. 575-582 ◽  
Author(s):  
Evgenii Kuznetsov ◽  
Sergey Leonov ◽  
Dmitry Tarkhov ◽  
Alexander Vasilyev
Keyword(s):  
Neural Network ◽  
Experimental Data ◽  
Parameter Identification ◽  
Uniaxial Tension ◽  
Network Modeling ◽  
Identification Problem ◽  
Neural Network Modeling ◽  
Creep Theory ◽  
Parameter Identification Problem ◽  
Kinetic Creep

The paper deals with a parameter identification problem for creep and fracture model. The system of ordinary differential equations of kinetic creep theory is applied for describing this model. As for solving the parameter identification problem, we proposed to use the technique of neural network modeling, as well as the multilayer approach. The procedures of neural network modeling and multilayer approximation constructing application is demonstrated by the example of finding parameters for uniaxial tension model for isotropic steel 45 specimens at creep conditions. The solution corresponding to the obtained parameters agrees well with theoretical strain-damage characteristics, experimental data, and results of other authors.

The parameter identification problem for the somatic shunt model

1992 ◽  
Vol 66 (4) ◽  
pp. 307-318 ◽  
Author(s):  
John A. White ◽  
Paul B. Manis ◽  
Eric D. Young
Keyword(s):  
Parameter Identification ◽  
Identification Problem ◽  
Parameter Identification Problem
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