Geodesic
Rapid “algebraic” Fourier transforms on uniformly distributed meshes
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2016), pp. 93-98 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: ideal, mesh, characteristic function of mesh, meshes uniformly distributed on multidimensional unit cube, critical mesh, critical determinant.
Mots-clés : discrete Fourier transform (DFT), rapid Fourier transform (RFT) 
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     title = {Rapid {\textquotedblleft}algebraic{\textquotedblright} {Fourier} transforms on uniformly distributed meshes},
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}
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Zh. N. Temirgaliyeva; N. Temirgaliyev. Rapid “algebraic” Fourier transforms on uniformly distributed meshes. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2016), pp. 93-98. http://geodesic.mathdoc.fr/item/IVM_2016_5_a8/

[1] Cooley J. W., Tukey J. W., “An algorithm for the machine calculation of complex Fourier series”, Mathematics of Computation, 19:90 (1965), 297–301 | DOI | MR | Zbl

[2] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. N., Chislennye metody, BINOM. Laboratoriya znanii, M., 2007

[3] Temirgaliev N., “Primenenie teorii divizorov k chislennomu integrirovaniyu periodicheskikh funktsii mnogikh peremennykh”, Matem. sb., 181:4 (1990), 490–505 | MR | Zbl

[4] Bailov E. A., Sikhov M. B., Temirgaliev N., “Ob obschem algoritme chislennogo integrirovaniya funktsii mnogikh peremennykh”, Zhurn. vychisl. matem. i matem. fiz., 54:7 (2014), 1059–1077 | DOI | MR | Zbl

[5] Zhubanysheva A. Zh., Temirgalieva Zh. N., Temirgaliev N., “Primenenie teorii divizorov k postroeniyu tablits optimalnykh koeffitsientov kvadraturnykh formul”, Zhurn. vychisl. matem. i matem. fiz., 49:1 (2009), 14–25 | MR | Zbl

[6] Gekke E., Lektsii po teorii algebraicheskikh chisel, GITTL, M.–L., 1940

[7] Gruber P. M., Lekkerkerker K. G., Geometriya chisel, Per. s angl., Nauka, M., 2008

[8] Nussbaumer G., Bystroe preobrazovanie Fure i algoritmy vychisleniya svertok, Per. s angl., Radio i svyaz, M., 1985 | MR

[9] Bleikhut R., Bystrye algoritmy tsifrovoi obrabotki signalov, Per. s angl., Mir, M., 1989 | MR

[10] Wang Yuan, “Number theoretic method in numerical analysis”, Contemporary Mathematics, 77 (1988), 63–82 | DOI | MR | Zbl

[11] Rader C. M., “Discrete Fourier transforms when the number of data samples is prime”, Proc. IEEE, 56:6 (1968), 1107–1108 | DOI