Examples



mdbootstrap.com



 
Статья
2016

Rapid “algebraic” Fourier transforms on uniformly distributed meshes


Zh. N. TemirgalievaZh. N. Temirgalieva, N. TemirgalievN. Temirgaliev
Русская математика
https://doi.org/10.3103/S1066369X16050091
Abstract / Full Text

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.

Author information
  • University of Southern California, Los Angeles, CA, USAZh. N. Temirgalieva
  • L. N. Gumilyov Eurasian National University, ul. Satpaeva 2, Astana, 010008, Republic of KazakhstanN. Temirgaliev
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).
  2. Bakhvalov, N. S., Zhidkov, N. P., Kobel’kov, G. N. Numerical Methods (BINOM. Laboratory of Knowledge, Moscow, 2007) [in Russian].
  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).
  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).
  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).
  6. Hecke, E. Lectures on Theory of Algebraic Numbers (GITTL, Moscow–Leningrad, 1940) [Russian translation].
  7. Lekkerkerker, C. G., Gruber, P. Geometry of Numbers (Elsevier, 1987).
  8. Nussbaumer, H. J. Fast Fourier Transform and Convolution Algorithms (Springer Series in Information Sciences, 1982).
  9. Blahut, R. E. Fast Algorithms for Digital Signal Processing (Addison-Wesley Publishing Company, 1985).
  10. Wang, Yuan. “Number Theoretic Method in Numerical Analysis”, Contemporary Mathematics 77, 63–82 (1988).
  11. Rader, C. M. “Discrete Fourier Transforms when the Number of Data Samples is Prime”, Proc. IEEE 56, No. 6, 1107–1108 (1968).