Multidimensional Fourier interpolation and complexity of the fast Fourier transform
https://doi.org/10.22405/2226-8383-2024-25-4-42-52
Abstract
Доказано равенство коэффициентов интерполяционного многочлена по параллелепипедальной сетке для многомерной функции коэффициентам интерполяционного многочлена
по равномерной сетке для одномерной функции, для получения которых можно применить быстрое преобразование Фурье по различным схемам.
Keywords
Parallelepipedal grid,
linear comparison solution lattice,
interpolation polynomial,
fast Fourier transform.
Supporting agencies: The work was carried out within the framework of the state assignment of the Ministry of Education of the Russian Federation, the topic of scientific research is “Number-theoretic methods in approximate analysis and their applications in mechanics and physics”.
About the Authors
Yuri Alexandrovich Basalov
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Viktor Alekseevich Bykovskii
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, corresponding member of the Russian Academy of Sciences, professor
Nikolai Nikolaevich Dobrovol’skii
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Vladimir Nikolaevich Chubarikov
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
Nikolai Mikhailovich Dobrovol’skii
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
1. Basalov, Yu.A., Dobrovol’skii, N.N. & Chubarikov, V.N. 2024, “Multidimensional Fourier interpolation and fast Fourier transforms”, Dokl. Math.,
2. Bocharova, L.P., Van’kova, V.S. & Dobrovol’skii, N.M. 1991, “On the calculation of optimal coefficients”, Matematicheskie zametki, vol. 49, no. 2, pp. 23–28.
3. Bykovskij, V.А 1988, “Discrete Fourier transform and cyclic convolution on integer lattices”, Matematicheskij sbornik, vol. 136(178), no. 4(8), pp. 451–467.
4. Dobrovol’skii, N.M., Yesayan, A.R., Andreeva, O.V., Zaitseva, N.V. 2004, “Multidimensional number-theoretic Fourier interpolation”, Chebyshevskii sbornik, vol. 5, iss. 1(9), pp. 122–143.
5. Dobrovol’skii, N.M. & Klepikova, N.L. 1990, “Table of optimal coefficients for approximate calculation of multiple integrals”, Institut obshhej fiziki АN SSSR, Moscow, USSR.
6. Korobov, N.M. 1959, “On approximate computation of multiple integrals”, Doklady Аkademii nauk SSSR, vol. 124, no. 6, pp. 1207–1210.
7. Korobov, N.M. 1959, “The evaluation of multiple integrals by method of optimal coefficients”, Vestnik Moskovskogo universiteta, no. 4, pp. 19–25.
8. Korobov, N.M. 1960, “Properties and calculation of optimal coefficients”, Doklady Аkademii nauk SSSR, vol. 132, no. 5, pp. 1009–1012.
9. Korobov, N.M. 1963, O teoretiko-chislovykh metodakh v priblizhennom analize [On numbertheoretic methods in approximate analysis], Mashgiz, Moscow, Russia.
10. Korobov, N.M. 1982, “On the calculation of optimal coefficients”, Doklady Аkademii nauk SSSR, vol. 267, no. 2, pp. 289–292.
11. Korobov, N.M. 2004, “Teoretiko-chislovye metody v priblizhennom analize”, [Number-theoretic methods in approximate analysis], 2nd ed, MTSNMO, Moscow, Russia.
12. Nussbaumer, H., 1985, “Fast Fourier Transform and Convolution Algorithms”, M.: Radiocommunication.
13. Rodionov, A.V., Dobrovol’skii, M.N., Dobrovol’skii, N.N., Dobrovol’skii, N.M. 2023, “Interpolation for a system of concentric grids”, Chebyshevskii sbornik, vol. 24, no. 3, pp. 95–121.
14. Ryaben’kij, V.S., 1960, “On tables and interpolation of functions from a certain class”, Doklady Аkademii nauk SSSR, vol. 131, no. 5, pp. 1025–1027.
15. Hlawka, E., 1962, “Zur angen¨aherten Berechnung mehrfacher Integrale”, Monatshefte f¨ur Mathematik, 66, pp. 140–151.
16. Rader, C., 1968, “Discrete Fourier Transforms when the Number of Data Points is Prime”, Proc. IEEE 56, pp. 1107–1108.
17. Temlyakov, V., 2018, “Multivariate approximation”, Cambridge Monogr. Appl. Comput. Math., 32, Cambridge University Press, Cambridge, 550 pp.
Review
For citations:
Basalov Yu.A., Bykovskii V.A., Dobrovol’skii N.N., Chubarikov V.N., Dobrovol’skii N.M. Multidimensional Fourier interpolation and complexity of the fast Fourier transform. Chebyshevskii Sbornik. 2024;25(4):42-52. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-4-42-52
Views:
78
Email this article 