To numerical solution of problem on mean-square approximation of real nonnegative finite function with respect to two variables by module of double fourier transformation

Author

Savenko, P.O. ; Tkach, M.D.

Author_Institution

Pidstryhach Inst. for Appl. Problems of Mech. & Math., Lviv

fYear

2007

fDate

17-21 Sept. 2007

Firstpage

193

Lastpage

195

Abstract

A nonlinear problem on mean-square approximation of a real finite nonnegative continuous function with respect to two variables by the module of double Fourier integral dependent on two parameters is investigated. Finding the optimum solutions (prototypes of Fourier integral) is reduced to investigation and numerical solution of Hammerstein type nonlinear two-dimensional integral equation. Algorithms for numerical finding the lines of branching and branching-off solutions to this equation are constructed and justified. Numerical examples are given.

Keywords

Fourier transforms; integral equations; mean square error methods; nonlinear equations; 2D integral equation; Fourier integral; Hammerstein type nonlinear integral equation; double Fourier transformation; finite nonnegative continuous function; mean-square approximation; real nonnegative finite function; Acoustics; Antenna theory; Approximation algorithms; Gold; Hilbert space; Integral equations; Inverse problems; Mathematics; Nonlinear equations; Prototypes; Nonlinear spectral problem; continuous components of spectrum; holomorphic operator-function; implicit function method;

fLanguage

English

Publisher

ieee

Conference_Titel

Antenna Theory and Techniques, 2007 6th International Conference on

Conference_Location

Sevastopol

Print_ISBN

978-1-4244-1584-7

Type

conf

DOI

10.1109/ICATT.2007.4425154

Filename

4425154