Mathematics – Commutative Algebra
Scientific paper
2010-01-08
Mathematics
Commutative Algebra
15 pages, 4 figures, submitted to JSC
Scientific paper
As is well known, the geometry of the interpolation site of a multivariate polynomial interpolation problem constitutes a dominant factor for the structures of the interpolation polynomials. Solving interpolation problems on interpolation sites with special geometries in theory may be a key step to the development of general multivariate interpolation theory. In this paper, we introduce a new type of 2-dimensional interpolation sites, tower interpolation sites, whose associated degree reducing Lagrange interpolation monomial and Newton bases w.r.t. fixed standard term orders such as lexicographical order, total degree lexicographical order, etc. can be figured out theoretically. Inputting these interpolation bases into Buchberger-M\"oller(BM) algorithm, we can also construct the reduced Gr\"{o}bner bases for related vanishing ideals. Experimental results show that in this way we can get the bases much faster than inputting tower sites directly into BM algorithm.
Chen Tairong
Dong Tian
Wang Xiaoying
Zhang Shugong
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