An estimation method for the number of point masses in an inverse logarithmic potential problem using discrete Fourier transform

A numerical method is discussed for the estimation of the number of point masses in an inverse logarithmic potential problem. We consider the case of some pieces of point masses being located in an “indeterminacy domain”, and consider a problem to estimate the number of point masses using observatio...

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Bibliographic Details
Published in:Applied mathematical modelling 1995-07, Vol.19 (7), p.429-436
Main Authors: Ohe, Takashi, Ohnaka, Kohzaburo
Format: Article
Language:English
Subjects:
Algorithms for functional approximation
boundary observation
criterion function
discrete Fourier transform
Exact sciences and technology
Fourier analysis
Function theory, analysis
inverse logarithmic potential problem
Mathematical analysis
Mathematical methods in physics
Mathematics
number of point masses
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation and analysis
Physics
point mass model
Potential theory
Sciences and techniques of general use
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Summary:A numerical method is discussed for the estimation of the number of point masses in an inverse logarithmic potential problem. We consider the case of some pieces of point masses being located in an “indeterminacy domain”, and consider a problem to estimate the number of point masses using observation data of the logarithmic potential on the boundary. A uniqueness theorem is derived for this problem from an algebraic relation between parameters of a point mass model and Fourier coefficients of the logarithmic potential. Applying this theorem, we propose a numerical method for our problem using a criterion function computed from the discrete Fourier transform. The applicability of our method is illustrated by numerical examples.
ISSN:0307-904X
DOI:10.1016/0307-904X(94)00037-7