On the linear independence of the derivatives of Bernstein polynomials

On the linear independence of the derivatives of Bernstein polynomials

We prove that any μrth order derivatives of degree-n Bernstein polynomials are linearly independent if and only if μ≤n−r+1, where r∈{1,2,…,n}.

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Veröffentlicht in:Journal of computational and applied mathematics 2022-07, Vol.408, p.114102, Article 114102
Hauptverfasser: Lu, Lizheng, Li, Lin
Format: Artikel
Sprache:eng
Schlagworte:
Bernstein basis
Derivatives of Bernstein polynomials
Linear independence
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Beschreibung
Zusammenfassung:We prove that any μrth order derivatives of degree-n Bernstein polynomials are linearly independent if and only if μ≤n−r+1, where r∈{1,2,…,n}.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2022.114102