Abstract
Multivariate ideal interpolation schemes are deeply connected with H-bases. Both the definition of a H-basis and of an ideal interpolation space depend of the notion of degree used in the grading decomposition of the polynomial spaces. We studied, in the case of bivariate polynomials, a generalized degree, introduced by T. Sauer and named w-degree. This article give some theoretical results that allow us to construct algorithms for calculus of the dimension of the homogeneous spaces of bivariate polynomials of w – degree n. We implemented these algorithms in C++ language. The analysis of the results obtained, leads us to another theoretical conjecture which we proved in the end.
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References
Sauer, T.: Gröbner basis, H-basis and interpolation. Transactions of the American Mathematical Society (1994) (html paper)
Sauer, T.: Polynomial interpolation of minimal degree and Gröbner bases. In: Gröbner Bases and Applications (Proc. of the Conf. 33 Year of Gröbner Bases). London Math. Soc., Lecture Notes, vol. 251, pp. 483–494 (1998)
Möller, H.M., Sauer, T.: H-bases for polynomial interpolation and system solving. Advances in Computational Mathematics (1999) (html paper)
Simian, D.: Multivariate interpolation from polynomial subspaces of w-degree n. In: Mathematical Analysis and Approximation Theory. Proceedings of the 5th Romanian - German Seminar on Approximation Theory and its Applications, pp. 243–254. Burg-Verlag (2002)
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Simian, D., Simian, C., Moiceanu, A. (2005). Computational Aspects in Spaces of Bivariate Polynomial of w-Degree n . In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_59
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DOI: https://doi.org/10.1007/978-3-540-31852-1_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24937-5
Online ISBN: 978-3-540-31852-1
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