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Optimal numerical integration on a sphere. (English) Zbl 0233.65016

MSC:
65D30 Numerical integration
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[1] B. A. Ditkin, “Some approximate formulae for evaluating triple integrals,” Dokl. Akad. Nauk SSSR, v. 62, 1948, p. 445-7.
[2] C. Finden, Spherical integration, Dissertation submitted for the Diploma in Numerical Analysis and Automatic Computing, University of Cambridge, 1961.
[3] Preston C. Hammer and Arthur H. Stroud, Numerical evaluation of multiple integrals. II, Math. Tables Aids Comput. 12 (1958), 272 – 280. · Zbl 0091.12302
[4] Volker Heine, Group theory in quantum mechanics, Pergamon Press, Oxford-New York-Toronto, Ont., 1977. An introduction to its present usage; Third revised reprinting; International Series in Natural Philosophy, Vol. 91. · Zbl 0089.18502
[5] D. G. Kendall, “Gaussian integration on the sphere,” Unpublished Report to the Atlas Computer Laboratory, 1962.
[6] Walter Ledermann, Introduction to the theory of finite groups, Oliver and Boyd, Edinburgh and London; Interscience Publishers, Inc., New York, 1953. 2d ed.
[7] L. A. Lyusternik & B. A. Ditkin, “Construction of approximate formulae for evaluating multiple integrals,” Dokl. Akad. Nauk SSSR, v. 61, 1948, p. 441-4.
[8] L. A. Lyusternik, “Some cubature formulae for repeated integrals,” Dokl. Akad. Nauk SSSR, v. 62, 1948, p. 449-52.
[9] William H. Peirce, Numerical integration over the spherical shell, Math. Tables Aids Comput 11 (1957), 244 – 249. · Zbl 0084.34905
[10] S. L. Sobolev, Formulas for mechanical cubatures in \?-dimensional space, Dokl. Akad. Nauk SSSR 137 (1961), 527 – 530 (Russian). · Zbl 0196.49202
[11] S. L. Sobolev, Various types of convergence of cubature and quadrature formulas, Dokl. Akad. Nauk SSSR 146 (1962), 41 – 42 (Russian). · Zbl 0126.31804
[12] S. L. Sobolev, Cubature formulas on the sphere which are invariant under transformations of finite rotation groups, Dokl. Akad. Nauk SSSR 146 (1962), 310 – 313 (Russian).
[13] S. L. Sobolev, On the number of nodes of cubature formulae on a sphere, Dokl. Akad. Nauk SSSR 146 (1962), 770 – 773 (Russian).
[14] G. Szegö, Orthogonal Polynomials, Colloquium Publications, v. 23, American Mathematical Society, 1959. · Zbl 0089.27501
[15] Hermann Weyl, Symmetry, Princeton University Press, Princeton, N. J., 1952. · Zbl 0046.00406
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