Applied Nonlinear Ill-Posed Problems and the Variational Approach for Constructing of Regularizing Algorithms

1998 ◽  
pp. 201-210
Author(s):  
I. V. Kochikov ◽  
G. M. Kuramshina ◽  
A. G. Yagola
Keyword(s):  
Variational Approach ◽  
Regularizing Algorithms ◽  
Ill Posed

On a characteristic property of conditionally well-posed problems

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Mikhail Y. Kokurin
Keyword(s):  
Inverse Problems ◽  
Input Data ◽  
Characteristic Property ◽  
Optimization Problems ◽  
Data Driven ◽  
Error Models ◽  
Regularizing Algorithms ◽  
Stochastic Error ◽  
Ill Posed ◽  
Well Posed

AbstractThe aim of this paper is to discuss and illustrate the fact that conditionally well-posed problems stand out among all ill-posed problems as being regularizable via an operator independent of the level of errors in input data. We give examples of corresponding purely data driven regularizing algorithms for various classes of conditionally well-posed inverse problems and optimization problems in the context of deterministic and stochastic error models.

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