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Superposition interpolation process in Cn
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DOI：10.1016/j.amc.2009.04.079.png)
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摘要
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In this paper, we deeply research Lagrange interpolation by polynomial in several variables and give an application of Cayley-Bacharach theorem for it. Particularly on the sufficiently intersected algebraic manifold (or SIAM, for short), we introduce a general method of constructing properly posed set of nodes (or PPSN, for short) for Lagrange interpolation, namely the superposition interpolation process. Then we give an equivalent condition about a PPSN along a SIAM. Further we introduce a relation between the sufficiently intersected algebraic hypersurfaces and H-basis. At the end of this paper, we use the extended Cayley-Bacharach theorem to resolve some problems of Lagrange interpolation along the zero-dimensional and one-dimensional algebraic manifolds. (C) 2009 Elsevier Inc. All rights reserved.
Keyword:
Multivariate Lagrange interpolation
Lagrange interpolation along an algebraic manifold
Properly posed set of nodes for Lagrange interpolation
Superposition interpolation process
Cayley-Bacharach theorem
期刊
IF:
3.4
论文数:
2.3W
被引数:
3.3W
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