Bernstein polynomial/Definition
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Revision as of 10:44, 25 November 2016 by Alec (Talk | contribs) (Created page with "<noinclude> __TOC__ ==Definition== </noinclude>The {{M|n}}<sup>th</sup> ''Bernstein polynomial'' for a function {{M|f:I\rightarrow\mathbb{R} }} (where {{M|I:\eq[0,1]\subset\ma...")
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Definition
The [ilmath]n[/ilmath]th Bernstein polynomial for a function [ilmath]f:I\rightarrow\mathbb{R} [/ilmath] (where [ilmath]I:\eq[0,1]\subset\mathbb{R} [/ilmath] is the closed unit interval) is defined as follows:
- [math]\mathcal{B}_n(f;x):\eq\sum^n_{i\eq 0}{}^nC_if\left(\tfrac{k}{n}\right)x^i(1-x)^{n-i} [/math]
References
