| 关于n维单形保多项式超限插值的表示问题 |
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| 引用本文： | 吕伟,汪国昭,梁友栋. 关于n维单形保多项式超限插值的表示问题[J]. 计算数学, 1991, 13(2): 145-152 |
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| 作者姓名： | 吕伟 汪国昭 梁友栋 |
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| 作者单位： | 浙江大学(吕伟，汪国昭)，浙江大学(梁友栋) |
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| 摘 要： | 以R~n表示n维欧氏空间,Z_+~n是R~n中坐标均为非负整数的全体,e~s为Z_+~(n+1)中第s个坐标为1其余坐标为0的单位向量;π_d(R~n)为全次数不大于d的n元多项式全体,
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| 关 键 词： | 超限插值 多项式插值 显式表示 |
ON THE REPRESENTATIONS OF POLYNOMIAL-PRESERVING TRANSFINITE INTERPOLANTS FOR SIMPLEX IN R~n |
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| Affiliation: | Lu Wei;Wang Guo-zhao;Liang You-dong Zhejing University |
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| Abstract: | In this paper, some new results about polynomial-preserving transfinite interpolation oversimplex in R~n are obtained, which include the necessary and sufficient conditions for the existen-ce of a polynomial interpolant and the minimal degree for polynomial interpolants, the repre-sentation of the interpolant, and the dimension of the interpolant space. Several applicationsof our results, such as in triangularized data interpolation and multivariate splines, are discus-sed. |
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