Homogeneous numerical cubature formulas of interpolatory type

Authors

  • Gheorghe Coman “Babes-Bolyai” University, Cluj-Napoca, Romania
  • Maria Solomon AISTEDA University, Faculty of Management, Alba Iulia, Romania

DOI:

https://doi.org/10.33993/jnaat311-707

Keywords:

interpolation, cubature formulas, multivariate approximation, homogeneous cubature, numerical cubature
Abstract views: 189

Abstract

In this paper we construct homogeneous numerical cubature formulas based on some numerical multivariate interpolation schemes.

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References

Barnhill, R. E. and Mansfield, L., Error bounds for smooth interpolation in triangles, J. Approx. Theory, 11, pp. 306-318, 1974, https://doi.org/10.1016/0021-9045(74)90002-1 DOI: https://doi.org/10.1016/0021-9045(74)90002-1

Coman, Gh., Multivariate approximation schemes and the approximation of linear functions, Mathematica, 16 (39), no. 2, pp. 229-249, 1974.

Coman, Gh., The complexity of the quadrature formulas, Mathematica (Cluj), 23 (46), pp. 183-192, 1981.

Coman, Gh., Homogeneous cubature formulas, Studia Univ. Babeş-Bolyai, Mathematica, 38, no. 2, pp. 91-101, 1993.

Delvos, F. F., Boolean methods for double integration, Math. Comp., 55, pp. 683-692, 1990, https://www.ams.org/journals/mcom/1990-55-192/S0025-5718-1990-1035928-7/S0025-5718-1990-1035928-7.pdf DOI: https://doi.org/10.1090/S0025-5718-1990-1035928-7

Sard, A., Linear Approximation, Amer. Math. Society, Providence, 1963. DOI: https://doi.org/10.1090/surv/009

Schoenberg, I. J., On best approximation of linear operators, Indag. Math., 26, pp. 155-163, 1964. DOI: https://doi.org/10.1016/S1385-7258(64)50018-9

Smolyak, S. A., Quadrature and interpolation formulas for tensor products of certain classes of functions, Soviet Math. Dokl., 4, pp. 240-243, 1963.

Somogyi, I., Almost optimal numerical methods, Studia Univ. Babeş-Bolyai, Mathematica, 1, pp. 85-93, 1999.

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Published

2002-02-01

How to Cite

Coman, G., & Solomon, M. (2002). Homogeneous numerical cubature formulas of interpolatory type. Rev. Anal. Numér. Théor. Approx., 31(1), 45–53. https://doi.org/10.33993/jnaat311-707

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