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Linear least squares method in nonlinear parametric inverse problems. (English) Zbl 07189032
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.
MSC:
65C60 Computational problems in statistics (MSC2010)
65D10 Numerical smoothing, curve fitting
90-08 Computational methods for problems pertaining to operations research and mathematical programming
Software:
KELLEY
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