Linear least squares method in nonlinear parametric inverse problems

A generalization of the linear least squares method to a wide class of parametric nonlinear inverse problems is presented. The approach is based on the consideration of the operator equations, with the selected function of parameters as the solution. The generalization is based on the two mandatory...

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Bibliographic Details
Published inJournal of inverse and ill-posed problems Vol. 28; no. 2; pp. 307 - 312
Main Author Frumin, Leonid L.
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.04.2020
Walter de Gruyter GmbH
Subjects
65C60
65D10
90-08
Inverse problems
Least squares method
Linear least squares method
Mathematical analysis
nonlinear parametric inverse problem
Operators (mathematics)
Parameter estimation
Transcendental functions
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Summary:A generalization of the linear least squares method to a wide class of parametric nonlinear inverse problems is presented. The approach is based on the consideration of the operator equations, with the selected function of parameters as the solution. The generalization is based on the two mandatory conditions: the operator equations are linear for the estimated parameters and the operators have discrete approximations. Not requiring use of iterations, this approach is well suited for hardware implementation and also for constructing the first approximation for the nonlinear least squares method. The examples of parametric problems, including the problem of estimation of parameters of some higher transcendental functions, are presented.
ISSN:0928-0219
1569-3945
DOI:10.1515/jiip-2019-0009