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Rapid “algebraic” Fourier transforms on uniformly distributed meshes

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Abstract

Based on algebraic theory of number, we determine discrete Fourier transforms with further concrete definitions. At that, the sets of specification of discrete function are interconnected with various optimization problems, quasi-Monte Carlo method including.

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References

  1. Cooley, J. W. and Tukey, J. W. “An Algorithm for the Machine Calculation of Complex Fourier Series”, Mathematics of Computation 19, No. 90, 297–301 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  2. Bakhvalov, N. S., Zhidkov, N. P., Kobel’kov, G. N. Numerical Methods (BINOM. Laboratory of Knowledge, Moscow, 2007) [in Russian].

    MATH  Google Scholar 

  3. Temirgaliev, N. “Application of Ideal Theory to the Numerical Integration of Periodic Functions of Several Variables”, Math.USSR, Sb. 69, No. 2, 527–542 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  4. Bailov, E. A., Sikhov, M. B., Temirgaliev, N. “General Algorithm for the Numerical Integration of Functions of Several Variables”, Comput. Math. Math. Phys. 54, No. 7, 1061–1078 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  5. Zhubanysheva, A. Zh., Temirgaliev, N., Temirgalieva, Zh. N. “Application of Divisor Theory to the Construction of Tables of Optimal Coefficients for Quadrature Formulas”, Comput. Math., Math. Phys. 49, No. 1, 12–22 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  6. Hecke, E. Lectures on Theory of Algebraic Numbers (GITTL, Moscow–Leningrad, 1940) [Russian translation].

    Google Scholar 

  7. Lekkerkerker, C. G., Gruber, P. Geometry of Numbers (Elsevier, 1987).

    MATH  Google Scholar 

  8. Nussbaumer, H. J. Fast Fourier Transform and Convolution Algorithms (Springer Series in Information Sciences, 1982).

    Book  MATH  Google Scholar 

  9. Blahut, R. E. Fast Algorithms for Digital Signal Processing (Addison-Wesley Publishing Company, 1985).

    MATH  Google Scholar 

  10. Wang, Yuan. “Number Theoretic Method in Numerical Analysis”, Contemporary Mathematics 77, 63–82 (1988).

    Article  MathSciNet  Google Scholar 

  11. Rader, C. M. “Discrete Fourier Transforms when the Number of Data Samples is Prime”, Proc. IEEE 56, No. 6, 1107–1108 (1968).

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Southern California, Los Angeles, CA, USA

    Zh. N. Temirgalieva

  2. L. N. Gumilyov Eurasian National University, ul. Satpaeva 2, Astana, 010008, Republic of Kazakhstan

    N. Temirgaliev

Authors
  1. Zh. N. Temirgalieva
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  2. N. Temirgaliev
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Corresponding authors

Correspondence to Zh. N. Temirgalieva or N. Temirgaliev.

Additional information

Original Russian Text © Zh.N. Temirgalieva, N. Temirgaliev, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 5, pp. 93–98.

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Temirgalieva, Z.N., Temirgaliev, N. Rapid “algebraic” Fourier transforms on uniformly distributed meshes. Russ Math. 60, 81–85 (2016). https://doi.org/10.3103/S1066369X16050091

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  • DOI: https://doi.org/10.3103/S1066369X16050091

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