Multidimensional Fourier Interpolation and Fast Fourier Transforms

Yu. A. Basalov^a^,*, N. N. Dobrovolsky^{a, b}^,**, and V. N. Chubarikov^b^,***

^aTula State Lev Tolstoy Pedagogical University, Tula, Russia

^bFaculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

email: *basalov_yurij@mail.ru
email: **nikolai.dobrovolsky@gmail.com
email: ***chubarik2020@mail.ru

Received 26 April, 2024

Abstract— It is proved that the coefficients of the interpolation polynomial over a parallelepipedal grid for a multidimensional function are equal to the coefficients of the interpolation polynomial over a uniform grid for a one-dimensional function. These coefficients can be obtained by applying the fast Fourier transform based on various schemes.

Keywords: parallelepipedal grid, linear congruence lattice, interpolation polynomial, fast Fourier transform

DOI: 10.1134/S1064562424702065