Geodesic
The Radon transform in the scheme C(N)D-inverstigations and the quasi-Monte Carlo theory
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2020), pp. 98-104.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article has a programmatic principles in the concept of studying the Radon transform according to the computational (numerical) diameter and applying the theory of uniform distribution. The principal result is that the Radon transforms are qualified as optimal among the all possible linear functionals that are used to extract numerical information for generating a computational aggregate.
Mots-clés : Radon transform
Keywords: computational (numerical) diameter, quasi-Monte Carlo method, recoveryof functions, limiting error. 
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N. Temirgaliyev; Sh. K. Abikenova; Sh. U. Azhgaliev; G. E. Taugynbaeyva. The Radon transform in the scheme C(N)D-inverstigations and the quasi-Monte Carlo theory. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2020), pp. 98-104. http://geodesic.mathdoc.fr/item/IVM_2020_3_a9/

[1] Radon J., “Uber die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Berichte uber die Verhandlungen Gesellshaft der Wissenschaften zu Leipzig”, J. Math. Phys., 69 (1917), 262–277 | Zbl

[2] The first 100 years of the Radon transform (Linz, Austria, 27–31 March, 1917) | Zbl

[3] Natterer F., The Mathematics of Computerized Tomography, Soc. for Industrial and Appl. Math., 2001 | MR

[4] Hetzenecker K., Limbeck-Lilienau C., Schweizer D., Laufersweiler B., Innovation durch Grundlagenforschung. Der Beitrag wissenschaftlicher Theorien und Entdeckungen zum gesamtgesellschaftlichen Fortschritt, Begleitheft zur Ausstellung an der Univ. Wien, 2016

[5] Temirgaliev N., Zhubanysheva A.Zh., “Teoriya priblizhenii, Vychislitelnaya matematika i Chislennyi analiz v novoi kontseptsii v svete Kompyuternogo (vychislitelnogo) poperechnika”, Vestn. Evraziisk. nats. un-ta im. L.N. Gumileva. Ser. Matem. Informatika. Mekhanika, 124:3 (2018), 8–88

[6] Temirgaliev N., Zhubanysheva A.Zh., “Kompyuternyi (vychislitelnyi) poperechnik v kontekste obschei teorii vosstanovleniya”, Izv. vuzov. Matem., 2019, no. 1, 89–97

[7] Temirgaliev N., Zhubanysheva A.Zh., “Poryadkovye otsenki norm proizvodnykh funktsii s nulevymi znacheniyami na lineinykh funktsionalakh i ikh primeneniya”, Izv. vuzov. Matem., 2017, no. 3, 89–95 | MR

[8] Triebel N., Interpolation theory, function spaces, differential operators, North-Holland Pub. Co., Amsterdam–New York, 1978 ; Tribel Kh., Teoriya interpolyatsii, funktsionalnye prostranstva, differentsialnye operatory, Mir, M., 1980 | MR | Zbl

[9] Azhgaliev Sh.U., Temirgaliev N., “Ob informativnoi moschnosti lineinykh funktsionalov”, Matem. zam., 73:6 (2003), 803–812 | DOI | MR | Zbl

[10] Temirgaliev N., Sherniyazov K.E., Berikkhanova M.E., “Tochnye poryadki kompyuternykh (vychislitelnykh) poperechnikov v zadachakh vosstanovleniya funktsii i diskretizatsii reshenii uravneniya Kleina–Gordona po koeffitsientam Fure”, Sovremen. probl. matem., 17, 2013, 179–207 | DOI

[11] Zhubanysheva A.Zh., Temirgaliev N., “Informativnaya moschnost trigonometricheskikh koeffitsientov Fure i ikh predelnaya pogreshnost pri diskretizatsii operatora differentsirovaniya na mnogomernykh klassakh Soboleva”, Zhurn. vychisl. matem. i matem. fiziki, 55:9 (2015), 1474–1485 | DOI | MR | Zbl

[12] Temirgaliev N., Abikenova Sh.K., Zhubanysheva A.Zh., Taugynbaeva G.E., “Zadachi diskretizatsii reshenii volnovogo uravneniya, chislennogo differentsirovaniya i vosstanovleniya funktsii v kontekste kompyuternogo (vychislitelnogo) poperechnika”, Izv. vuzov. Matem., 2013, no. 8, 86–93 | Zbl

[13] Korobov N.M., Teoretiko-chislovye metody v priblizhennom analize, Fizmatgiz, M., 1963

[14] Hua Loo Keng, Wang Yuan, Application of number theory of numerical analysis, Springer Verlag, New York, 1981 | MR

[15] Hlawka E., Firneis F., Zinterhof P., Zahlentheoretische Methoden in der numerischen Mathematik, Wien–München–Oldenbourg, 1981 | MR

[16] Bakhvalov N.S., “O priblizhennom vychislenii kratnykh integralov”, Vestn. MGU. Ser., Matem., mekhanika, 1959, no. 4, 3–18

[17] Plaskota L., Wozniakowski H., Monte Carlo and Quasi-Monte Carlo Methods, Springer Sci. Business Media, 2010 | MR

[18] Dick J., Pillichshammer F., Digital Nets and Sequences. Discrepancy Theory and Quasi-Monte Carlo Integration, Cambridge Univ. Press, Cambridge, 2010 | MR | Zbl

[19] Voronin S.M., Temirgaliev N., “O kvadraturnykh formulakh, svyazannykh s divizorami polya gaussovykh chisel”, Matem. zametki, 46:2 (1989), 34–41 | Zbl

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

[21] Bailov E.A., Zhubanysheva A.Zh., Temirgaliev N., “Ob obschem algoritme chislennogo integrirovaniya periodicheskikh funktsii mnogikh peremennykh”, Dokl. RAN, 416:2 (2007), 169–173 | MR | Zbl

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

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

[24] Sherniyazov K., Priblizhennoe vosstanovlenie funktsii i reshenii uravneniya teploprovodnosti s funktsiyami raspredeleniya nachalnykh temperatur iz klassov E, SW i B, Diss. ... kand. fiz.-matem. nauk, KazGU im. al-Farabi, 1998

[25] Temirgaliev N., “Kompyuternyi (vychislitelnyi) poperechnik. Algebraicheskaya teoriya chisel i garmonicheskii analiz v zadachakh vosstanovleniya (metod kvazi-Monte-Karlo). Teoriya vlozhenii i priblizhenii. Ryady Fure”, Vestn. Evraziisk. nats. un-ta im. L.N. Gumileva, 2010, Spets. vypusk, posvyaschennyi nauchnym dostizheniyam matematikov ENU im. L.N. Gumileva