Total Positivity of A Kind of Generalized Toric-Bernstein Basis

11/14/2018

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by   Ying-Ying Yu, et al.

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The normalized totally positive basis is a set of basis functions defined on the parameter domain Ξ, which satisfies the properties of non-negative and partition of the unit, meanwhile the collocation matrix of basis on arbitrary increasing real sequence is a totally positive matrix. Based on the generalized Vandermonde determinant defined on real points, the normalized total positivity of a kind of generalized toric-Bernstein basis is proved, which are defined on a set of real points.