Polovinkin, V. I. 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). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page 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 Keywords:asymptotically optimal formula; Sobolev spaces; periodic systems of nodes; asymptotic estimates for the error PDFBibTeX XMLCite \textit{V. I. Polovinkin}, Sib. Math. J. 22, 442--448 (1981; Zbl 0485.41029); translation from Sib. Mat. Zh. 22, 147--155 (1981) Full Text: DOI References: [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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.