Homogeneous numerical cubature formulas of interpolatory type
DOI:
https://doi.org/10.33993/jnaat311-707Keywords:
interpolation, cubature formulas, multivariate approximation, homogeneous cubature, numerical cubatureAbstract
In this paper we construct homogeneous numerical cubature formulas based on some numerical multivariate interpolation schemes.Downloads
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.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.