Geodesic
Normal bivariate Birkhoff interpolation schemes and Pell equation
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 2, pp. 265-272 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Finding the normal Birkhoff interpolation schemes where the interpolation space and the set of derivatives both have a given regular ``shape'' often amounts to number-theoretic equations. In this paper we discuss the relevance of the Pell equation to the normality of bivariate schemes for different types of ``shapes''. In particular, when looking at triangular shapes, we will see that the conjecture in Lorentz R.A., {\it Multivariate Birkhoff Interpolation\/}, Lecture Notes in Mathematics, 1516, Springer, Berlin-Heidelberg, 1992, is not satisfied, and, at the same time, we will describe the complete solution.
Finding the normal Birkhoff interpolation schemes where the interpolation space and the set of derivatives both have a given regular ``shape'' often amounts to number-theoretic equations. In this paper we discuss the relevance of the Pell equation to the normality of bivariate schemes for different types of ``shapes''. In particular, when looking at triangular shapes, we will see that the conjecture in Lorentz R.A., {\it Multivariate Birkhoff Interpolation\/}, Lecture Notes in Mathematics, 1516, Springer, Berlin-Heidelberg, 1992, is not satisfied, and, at the same time, we will describe the complete solution.
Classification : 11D09, 65D05
Keywords: Birkhoff interpolation; Pell equation 
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Crainic, Marius; Crainic, Nicolae. Normal bivariate Birkhoff interpolation schemes and Pell equation. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 2, pp. 265-272. http://geodesic.mathdoc.fr/item/CMUC_2009_50_2_a6/