We study the nonlinear problem of mean-square approximation of a real finite nonnegative continuous function of two variables by the modulus of a double Fourier integral depending on two parameters. The solution of this problem is reduced to the solution of a nonlinear two-dimensional integral equation of the Hammerstein type. Numerical algorithms for determination of branching lines and branched solutions of equation are constructed and substantiated. Some numerical examples are given.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 53–64, January–March, 2008.
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Savenko, P.O., Protsakh, L.P. & Tkach, M.D. On the best mean-square approximation of a real nonnegative finite continuous function of two variables by the modulus of a double Fourier integral. I. J Math Sci 160, 343–356 (2009). https://doi.org/10.1007/s10958-009-9502-3
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DOI: https://doi.org/10.1007/s10958-009-9502-3