Geodesic
Bivariate interpolation with integrals
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2009), pp. 26-31 Cet article a éte moissonné depuis la source Math-Net.Ru

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The bivariate interpolation problem, where the interpolation parameters are integrals over bounded regions, is considered in this paper. H. Hakopian posed a hypothesis for this problem in the case, when regions are obtained from intersection of lines in general position [2]. Till now the hypothesis is proved for polynomials of degree $\leq1$. In this paper we bring a new proof. Meanwhile we solve the problem in more general setting – in the case of arbitrary regions.
Keywords: correctness, bivariate
Mots-clés : centroid, interpolation. 
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G. A. Ktryan. Bivariate interpolation with integrals. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2009), pp. 26-31. http://geodesic.mathdoc.fr/item/UZERU_2009_2_a4/

[1] B.Bojanov, H. Hakopian, A. Sahakian, Spline Functions and Multivariate Interpolation, Kluwer Academic Publishers, 1993 | MR

[2] Kh. Rahsepar Fard, “An approach to interpolation by integration”, Proceedings of the YSU, Physics Mathematics, 2009, no. 2, 21–25