Deviation estimates for rational grids approximating algebraic
https://doi.org/10.22405/2226-8383-2022-23-4-170-177
Abstract
This paper is devoted to obtaining estimates of the deviation of a parallelepipedal grid, which is a rational grid approximating the algebraic grid of a quadratic field.
New tasks have been set for further research.
About the Authors
Nikolai Nikolaevich Dobrovol’skiiRussian Federation
candidate of physical and mathematical sciences
Irina Yuryevna Rebrova
Russian Federation
candidate of physical and mathematical sciences
Antonina Nikolaevna Kormacheva
Russian Federation
postgraduate student
Nikolai Mihailovich Dobrovol’skii
Russian Federation
doctor of physical and mathematical sciences, professor
References
1. Bakhvalov, N.S. 1959, “On approximate computation of multiple integrals”, Vestnik Moskovskogo
2. universiteta, no. 4, pp. 3–18.
3. Bykovskij, V.А 2002, “On the error of number-theoretic quadrature formulas”, Chebyshevskij
4. sbornik, vol. 3, no. 2(4), pp. 27–33.
5. O. A. Gorkusha, N. M. Dobrovolsky, 2005, "On estimates of hyperbolic zeta function of
6. lattices" // Chebyshevsky Collection, vol. 6, issue 2(14), pp. 130-138.
7. Dobrovol’skii, N. M. 1984, “Evaluation of generalized variance parallelepipedal grids”, Dep. v
8. VINITI, no. 6089–84.
9. Dobrovol’skii, N. M., Esayan, А.R., Pikhtil’kov, S.А., Rodionova, O.V. & Ustyan, А.E. 1999,
10. “On a single algorithm for finding optimal coefficients”, Izvestiya TulGU. Seriya Matematika.
11. Mekhanika. Informatika, vol. 5, no. 1, pp. 51–71.
12. Dobrovol’skii, N. M., Esayan, А.R. & Rebrova, I. YU. 1998, “On a recursive algorithm
13. for lattices”, Teoriya priblizhenij i garmonicheskij analiz: Tezisy doklada Mezhdunarodnoj
14. konferentsii (Approximation theory and harmonic analysis: proceedings of the International
15. conference), Tula, Russia.
16. Dobrovol’skii, N. M., Esayan, А.R. & Rebrova, I. YU. 1998, “On a recursive algorithm for
17. lattices”, Izvestiya TulGU. Seriya Matematika. Mekhanika. Informatika, vol. 5, no. 3, pp. 38–51.
18. Kassels, D. 1965, Vvedenie v geometriyu chisel, [Introduction to the geometry of numbers], Mir,
19. Moscow, Russia.
20. Kormacheva, A. N., 2019, "About the partial quotients of one of the continued fractions" ,
21. Chebyshevskii sbornik, vol. 20, no. 1, pp. 293–301.
22. A. N. Kormacheva, 2019, "Approximation of quadratic algebraic lattices by integer lattices" ,
23. Chebyshevskii sbornik, vol. 20, no. 2, pp. 366–373.
24. A. N. Kormacheva, 2020, "Approximation of quadratic algebraic lattices by integer lattices —
25. II" , Chebyshevskii sbornik, vol. 21, no. 3, pp. 215–222.
26. A. N. Kormacheva, N. N. Dobrovol’skii, N. M. Dobrovol’skii, 2021, “On the hyp erb olic
27. parameter of a two-dimensional lattice of comparisons”, Chebyshevskii sbornik, vol. 22, no.
28. , pp. 168–182.
29. Korobov, N.M. 1959, “The evaluation of multiple integrals by method of optimal coefficients”,
30. Vestnik Moskovskogo universiteta, no. 4, pp. 19–25.
31. Korobov, N.M. 1960, “Properties and calculation of optimal coefficients”, Doklady Аkademii
32. nauk SSSR, vol. 132, no. 5, pp. 1009–1012.
33. Mikhlyaeva, A. V., 2018, "Approximation of quadratic algebraic lattices and nets by integer
34. lattices and rational nets" , Chebyshevskii sbornik, vol. 19, no. 3, pp. 241–256.
35. Mikhlyaeva, A. V., 2019, "Quality function for the approximation of quadratic algebraic nets" ,
36. Chebyshevskii sbornik, vol. 20, no. 1, pp. 307–312.
37. Frolov, K.K. 1976, “Upper bounds on the error of quadrature formulas on classes of functions”,
38. Doklady Аkademii nauk SSSR, vol. 231, no.4, pp. 818–821.
Review
For citations:
Dobrovol’skii N.N., Rebrova I.Yu., Kormacheva A.N., Dobrovol’skii N.M. Deviation estimates for rational grids approximating algebraic. Chebyshevskii Sbornik. 2022;23(4):170-177. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-4-170-177