Numerical Approximation of Real Finite Nonnegative Function by the Modulus of Discrete Fourier Transform

DOI: 10.4236/am.2010.11008   PDF   HTML     3,715 Downloads   7,066 Views   Citations

Abstract

The numerical algorithms for finding the lines of branching and branching-off solutions of nonlinear problem on mean-square approximation of a real finite nonnegative function with respect to two variables by the modulus of double discrete Fourier transform dependent on two parameters, are constructed and justified.

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P. Savenko and M. Tkach, "Numerical Approximation of Real Finite Nonnegative Function by the Modulus of Discrete Fourier Transform," Applied Mathematics, Vol. 1 No. 1, 2010, pp. 65-75. doi: 10.4236/am.2010.11008.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] B. M. Minkovich and V. P. Jakovlev, “Theory of Synthesis of Antennas, ” Soviet Radio, Moscow, 1969.
[2] P. A. Savenko, “Numerical Solution of a Class of Nonlinear Problems in Synthesis of Radiating Systems,” Computational Mathematics and Mathematical Physics, Vol. 40, No. 6, 2000, pp. 889-899.
[3] P. O. Savenko, “Nonlinear Problems of Radiating Systems Synthesis (Theory and Methods of the Solution),” Institute for Applied Problems in Mechanics and Mathematics, Lviv, 2002.
[4] G. M. Vainikko, “Analysis of Discretized Methods,” Таrtus Gos. University of Tartu, Tartu, 1976.
[5] R. D. Gregorieff and H. Jeggle, “Approximation von Eigevwertproblemen bei nichtlinearer Parameterabh?ngi- keit,” Manuscript Math, Vol. 10, No. 3, 1973, pp. 245- 271.
[6] O. Karma, “Approximation in Eigenvalue Problems for Holomorphic Fredholm Operator Functions I,” Numerical Functional Analysis and Optimization, Vol. 17, No. 3-4, 1996, pp. 365-387.
[7] M. A. Aslanian and S. V. Kartyshev, “Updating of One Numerous Method of Solution of a Nonlinear Spectral Problem,” Journal of Computational Mathematics and Mathe- matical Physics, Vol. 37, No. 5, 1998, pp. 713-717.
[8] S. I. Solov’yev, “Preconditioned Iterative Methods for a Class of Nonlinear Eigenvalue Problems,” Linear Algebra and its Applications, Vol. 41, No. 1, 2006, pp. 210-229.
[9] P. A. Savenko and L. P. Protsakh, “Implicit Function Method in Solving a Two-dimensional Nonlinear Spectral Problem,” Russian Mathematics (Izv. VUZ), Vol. 51, No. 11, 2007, pp. 40-43.
[10] V. A. Trenogin, “Functional Analysis,” Nauka, Moscow ,1980.
[11] I. I. Privalov, “Introduction to the Theory of Functions of Complex Variables,” Nauka, Moscow, 1984.
[12] A. N. Kolmogorov and S. V. Fomin, “Elements of Functions Theory and Functional Analysis,” Nauka, Moscow, 1968.
[13] P. P. Zabreiko, А. I. Koshelev and М. А. Krasnoselskii, “Integral Equations,” Nauka, Moscow, 1968.
[14] М. А. Krasnoselskii, G. М. Vainikko, and P. P. Zabreiko, “Approximate Solution of Operational Equations,” Nauka, Moscow, 1969.
[15] I. I. Liashko, V. F. Yemelianow and A. K. Boyarchuk, “Bases of Classical and Modern Mathematical Analysis,” Vysshaya Shkola Publishres, Kyiv, 1988.
[16] E. Zeidler, “Nonlinear Functional Analysis and Its Appli- cations I: Fixed-Points Theorem,” Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1985.
[17] P. A. Savenko, “Synthesis of Linear Antenna Arrays by Given Amplitude Directivity Pattern,” Izv. Vysch. uch. zaved. Radiophysics, Vol. 22, No. 12, 1979, pp. 1498-1504.
[18] М. M. Vainberg and V. А. Trenogin, “Theory of Branching of Solutions of Nonlinear Equations,” Nauka, Moscow, 1969.
[19] V. V. Voyevodin and Y. J. Kuznetsov, “Matrices and Calcu- lations,” Nauka, Moscow, 1984.
[20] A. Gursa, “Course of Mathematical Analysis, Vol. 1, Part 1,” Moscow-Leningrad, Gos. Technical Theory Izdat, 1933.
[21] V. I. Smirnov, “Course of High Mathematics, Vol. 1,” Nauka, Moscow, 1965.

  
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