Scientific Research

An Academic Publisher

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

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.

Keywords

Share and Cite:

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.

[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. |

Copyright © 2020 by authors and Scientific Research Publishing Inc.

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.