Title :
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
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;
Conference_Titel :
Antenna Theory and Techniques, 2007 6th International Conference on
Conference_Location :
Sevastopol
Print_ISBN :
978-1-4244-1584-7
DOI :
10.1109/ICATT.2007.4425154
