One-Dimensional Inverse Problems

2020 ◽  
pp. 1-39
Author(s):  
Hiroshi Isozaki
Keyword(s):  
Inverse Problems ◽  
One Dimensional

Regularization of Some One-Dimensional Inverse Problems for Identification of Nonlinear Surface Phenomena

1995 ◽  
Author(s):  
C. W. Groetsch ◽  
Martin Hanke
Keyword(s):  
Inverse Problems ◽  
Model Identification ◽  
Surface Phenomena ◽  
Unbounded Operators ◽  
General Technique ◽  
Regularization Technique ◽  
One Dimensional ◽  
Data Errors ◽  
Ill Posed ◽  
Nonlinear Surface

Abstract A simple numerical method for some one-dimensional inverse problems of model identification type arising in nonlinear heat transfer is discussed. The essence of the method is to express the nonlinearity in terms of an integro-differential operator, the values of which are approximated by a linear spline technique. The inverse problems are mildly ill-posed and therefore call for regularization when data errors are present. A general technique for stabilization of unbounded operators may be applied to regularize the process and a specific regularization technique is illustrated on a model problem.

scholarly journals Inverse Problems for Time-Dependent Singular Heat Conductivities---One-Dimensional Case

2013 ◽  
Vol 45 (3) ◽  
pp. 1675-1690 ◽  
Author(s):  
P. Gaitan ◽  
H. Isozaki ◽  
O. Poisson ◽  
S. Siltanen ◽  
J. P. Tamminen
Keyword(s):  
Inverse Problems ◽  
Time Dependent ◽  
Dimensional Case ◽  
One Dimensional

Analysis of the Green’s function approach to one‐dimensional inverse problems. I. One parameter reconstruction

1993 ◽  
Vol 34 (12) ◽  
pp. 5724-5746 ◽  
Author(s):  
Sailing He ◽  
Sergei I. Kabanikhin ◽  
Vladimir G. Romanov ◽  
Staffan Ström
Keyword(s):  
Inverse Problems ◽  
Green’S Function ◽  
Green's Function ◽  
Function Approach ◽  
One Dimensional ◽  
Parameter Reconstruction
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