Some researches on multivariate Lagrange interpolation along the sufficiently intersected algebraic manifold |
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| Authors: | Jielin Zhang Xuezhang Liang Lihong Cui |
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| Affiliation: | 1. Department of Applied Mathematics , Dalian University of Technology , Dalian 116024, P.R. China jielinzh@dlut.edu.cn;3. Institute of Mathematics, Jilin University , Changchun, 130012, P.R. China;4. Institute of Mathematical Science, Liaoning Normal University , Dalian 116029, P.R. China |
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| Abstract: | In this article, Lagrange interpolation by polynomials in several variables is studied. Particularly on the sufficiently intersected algebraic manifolds, we discuss the dimension about the interpolation space of polynomials. After defining properly posed set of nodes (or PPSN for short) along the sufficiently intersected algebraic manifolds, we prove the existence of PPSN and give the number of points in PPSN of any degree. Moreover, in order to compute the number of points in PPSN concretely, we propose the operator ? k with reciprocal difference. |
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| Keywords: | Multivariate Lagrange interpolation PPSN Algebraic manifold Mathematics Subject Classifications 41A05 65D05 |
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