Regularization of the noisy Cauchy problem solution approximated by an energy-like method

SUMMARYThis paper focuses on the regularization of noisy Cauchy data and unknown boundary conditions approximated by the energy‐like minimization method. After providing considerations necessary for the numerical analysis leading to an adequate stopping criterion for the minimization process, we des...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2013-07, Vol.95 (4), p.271-287
Main Authors: Rischette, R., Baranger, T. N., Andrieux, S.
Format: Article
Language:English
Subjects:
Acoustic signal processing
Acoustics
Approximation
boundary conditions identification
Cauchy problem
Computer Science
data completion
denoising
Engineering Sciences
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical models
Mathematics
Mechanics
Minimization
noisy Cauchy problem
Numerical analysis
Optimization
Optimization and Control
Ordinary differential equations
Partial differential equations
Physics
Regularization
Reproduction
Sciences and techniques of general use
Signal and Image processing
Solid mechanics
stopping criterion
Thermics
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Summary:SUMMARYThis paper focuses on the regularization of noisy Cauchy data and unknown boundary conditions approximated by the energy‐like minimization method. After providing considerations necessary for the numerical analysis leading to an adequate stopping criterion for the minimization process, we describe the denoising procedure proposed. Numerical experiments involving singular data are presented.Copyright © 2013 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4501