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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Bibliographic Details
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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Summary: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.
ISBN:1509062696
9781509062690
9781509062706
150906270X
DOI:10.1109/PIERS.2017.8262370