Total Positivity of A Kind of Generalized Toric-Bernstein Basis

Total Positivity of A Kind of Generalized Toric-Bernstein Basis
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DOI：
10.1016/j.laa.2019.06.012
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发表时间：
2018-11
期刊：
ArXiv
影响因子：
--
通讯作者：
Yingying Yu;Hui Ma;Chungang Zhu
Yingying Yu;Hui Ma;Chungang Zhu
中科院分区：
其他
文献类型：
--
作者：
Yingying Yu;Hui Ma;Chungang Zhu

文献摘要

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规范化全正基在许多领域有着广泛的应用。基于广义Vandermonde行列式，证明了一类定义在真实的点集上的广义Toric-Bernstein基的归一化全正性.利用这一结果，得到了广义复曲面-Bézier曲线的渐进迭代逼近性质，并举例说明了这一性质.
The normalized totally positive bases are widely used in many fields. Based on the generalized Vandermonde determinant, the normalized total positivity of a kind of generalized toric-Bernstein basis is proved, which is defined on a set of real points. By this result, then the progressive iterative approximation property of the generalized toric-Bézier curve is obtained and some examples are provided to illustrate this property.