Aposteriori estimates in inverse problems for the Helmholtz equation

We consider the problem of estimation of the right-hand sides of the Helmholtz equation that models electromagnetic and acoustic wave fields when that initial data is uncertain. In the case when measurement errors depend on solutions, we construct algorithms of computation of the optimal estimates w...

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Published in2017 Progress In Electromagnetics Research Symposium - Spring (PIERS) pp. 3526 - 3531
Main Authors Nakonechny, A. G., Podlipenko, Y. K., Shestopalov, Y. V.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.05.2017
SeriesProgress in Electromagnetics Research Symposium
Subjects
Acoustic fields
Acoustic wave fields
Electromagnetics
Estimation
Helmholtz equation
Inverse problems
Linear algebra
Linear algebraic equation
Linear equations
Mathematical model
Measurement data
Measurement errors
Measurement uncertainty
Optimal estimates
Posteriori estimates
Right-hand sides
Springs
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Abstract We consider the problem of estimation of the right-hand sides of the Helmholtz equation that models electromagnetic and acoustic wave fields when that initial data is uncertain. In the case when measurement errors depend on solutions, we construct algorithms of computation of the optimal estimates which are compatible with the measurement data. It is shown that approximate a posteriori estimates of the right-hand sides are expressed via solutions of linear algebraic equations.
AbstractList We consider the problem of estimation of the right-hand sides of the Helmholtz equation that models electromagnetic and acoustic wave fields when that initial data is uncertain. In the case when measurement errors depend on solutions, we construct algorithms of computation of the optimal estimates which are compatible with the measurement data. It is shown that approximate a posteriori estimates of the right-hand sides are expressed via solutions of linear algebraic equations.
Author Podlipenko, Y. K.
Nakonechny, A. G.
Shestopalov, Y. V.
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  surname: Shestopalov
  fullname: Shestopalov, Y. V.
  organization: Univ. of Gavle, Gavle, Sweden
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Snippet We consider the problem of estimation of the right-hand sides of the Helmholtz equation that models electromagnetic and acoustic wave fields when that initial...
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Publisher
StartPage 3526
SubjectTerms Acoustic fields
Acoustic wave fields
Electromagnetics
Estimation
Helmholtz equation
Inverse problems
Linear algebra
Linear algebraic equation
Linear equations
Mathematical model
Measurement data
Measurement errors
Measurement uncertainty
Optimal estimates
Posteriori estimates
Right-hand sides
Springs
Title Aposteriori estimates in inverse problems for the Helmholtz equation
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