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Invariant Laplacian-involving cubature formulas

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Abstract

For integrals in n dimensions over a hypercube, two ninth-degree cubature formulas that are invariant with respect to a hyperoctahedral group are constructed. The cubature sums of these formulas contain the Laplacian. Examples are given in which approximate values of the formulas’ parameters are presented in the form of tables.

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References

  1. S. L. Sobolev, “On mechanical cubature formulas on a spherical surface,” Sib. Mat. Zh. 3(5), 769–791 (1962).

    MATH  Google Scholar 

  2. I. P. Mysovskikh, Interpolation Cubature Formulas (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

  3. V. I. Lebedev, “Quadratures on the sphere,” USSR Comput. Math. Math. Phys. 16(2), 10–24 (1976).

    Article  Google Scholar 

  4. G. N. Salikhov, Cubature Formulas for Multidimensional Spheres (FAN, Tashkent, 1986) [in Russian].

    Google Scholar 

  5. S. I. Konyaev, “On an invariant seventh-order quadrature formula for a spherically symmetric weight function,” in Problems in Mathematical Analysis (Krasnoyarsk. Gos. Tekh. Univ., Krasnoyarsk, 2001), Vol. 4, pp. 54–64 [in Russian].

    Google Scholar 

  6. S. B. Stoyanova, “A ninth-order accurate cubature formula for a hypercube,” Computational Methods (Sankt-Peterb. Gos. Univ., St. Petersburg, 2005), Vol. 21, pp. 172–179 [in Russian].

    Google Scholar 

  7. A. K. Ponomarenko, “On some invariant cubature formulas of seventh and ninth orders,” Proceeding of the 10th International Seminar on Cubature Formulas and Applications (Vost.-Sib. Gos. Univ. Tekhnol. Upr., Ulan-Ude, 2009), pp. 104–111.

    Google Scholar 

  8. G. N. Salikhov and F. Sharipkhodzhaeva, “Cubature formulas for evaluating integrals on the surface of a hyper-sphere,” Dokl. Akad. Nauk UzSSR, No. 6, 6–9 (1974).

    Google Scholar 

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Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034, Russia

    A. K. Ponomarenko

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  1. A. K. Ponomarenko
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Correspondence to A. K. Ponomarenko.

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Original Russian Text © A.K. Ponomarenko, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 2, pp. 179–184.

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Ponomarenko, A.K. Invariant Laplacian-involving cubature formulas. Comput. Math. and Math. Phys. 55, 169–174 (2015). https://doi.org/10.1134/S0965542515020153

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  • DOI: https://doi.org/10.1134/S0965542515020153

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