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Sequences of cubature formulas with periodic systems of nodes. (English. Russian original) Zbl 0485.41029

Sib. Math. J. 22, 442-448 (1982); translation from Sib. Mat. Zh. 22, 147-155 (1981).

MSC:

41A55 Approximate quadratures
65D30 Numerical integration
65D32 Numerical quadrature and cubature formulas
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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[1] S. L. Sobolev, ?Optimal formulas for mechanical cubature with nodes at the points of regular lattices,? Dokl. Akad. Nauk SSSR,164, No. 2, 281-284 (1965).
[2] S. L. Sobolev, Introduction to the Theory of Cubature Formulas [in Russian], Nauka, Moscow (1974).
[3] V. I. Polovinkin ?Cubature formulas in L 2 m (?),? Dokl. Akad. Nauk SSSR,190, No. 1, 42-44 (1970).
[4] V. I. Polovinkin, ?Asymptotic optimality of sequences of formulas with regular boundary layer for odd m,? Sib. Mat. Zh.,16, No. 2, 328-335 (1975). · Zbl 0339.65015
[5] V. I. Polovinkin, ?Asymptotically best sequences of cubature formulas,? Sib. Mat. Zh.,16, No. 6, 1255-1262 (1975).
[6] V. I. Polovinkin and L. I. Didur, ?Asymptotically optimal sequences of Hermitian cubature formulas,? Sib. Mat. Zh.,19, No. 3, 663-669 (1978).
[7] C. A. Rogers, Packing and Covering, Cambridge Univ. Press. · Zbl 0176.51402
[8] V. I. Polovinkin, ?Composite cubature formulas,? in: Problems of Computational and Applied Mathematics [in Russian], 14, Izd. Inst. Kibern. s Vych. Tsen. Akad. Nauk Uzb. SSR, Tashkent (1972). pp. 53-62.
[9] V. I. Polovinkin, ?Sequences of functionals with boundary layer,? Sib. Mat. Zh.,15, No. 2, 413-429 (1974).
[10] O. V. Besov, ?Intercellular averagings and error bounds for cubature formulas in S. L. Sobolev’s spaces and their generalizations,? Tr. Mat. Inst. Akad. Nauk SSSR,143, 42-57 (1977).
[11] V. I. Polovinkin, ?Certain estimates of the norms of error functionals for cubature formulas,? Mat. Zametki,5, No. 3, 317-322 (1969).
[12] S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, Amer. Math. Soc. (1969). · Zbl 0233.42013
[13] V. I. Polovinkin and L. I. Didur, ?On the order of convergence of cubature formulas,? in: Problems of Computational and Applied Mathematics [in Russian], Izd. Inst. Kibern. Vychisl. Tsentr. Akad. Nauk Uzb. SSR, Tashkent (1975), pp. 3-14.
[14] V. I. Polovinkin, ?Convergence of sequences of cubature formulas with boundary layer on concrete functions,? in: Mathematical Analysis and Connected Problems of Mathematics [in Russian], Nauka, Novosibirsk (1978), pp. 183-191.
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