Last Updated
：2025/12/03
Bernstein basis polynomial
Noun
Japanese Meaning
数学的解析および数値解析において、(t+(1-t))ⁿ の二項展開における各項、すなわち b_i,n(t)=組み合わせ(n,i) tⁱ(1-t)ⁿ⁻ⁱ の形で表される多項式基底。
（ plural ）
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(mathematical analysis, numerical analysis) Any polynomial of the form b_i,n(t)=n choose itⁱ(1-t)ⁿ⁻ⁱ!!, being the iᵗʰ term of the binomial expansion of (t+(1-t))ⁿ!.
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Bernstein basis polynomial
In approximation theory, the Bernstein basis polynomial b_{i,n}(t) = C(n,i) ti (1-t){n-i} is used to construct Bézier curves because of its positivity and partition of unity properties.
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In approximation theory, the Bernstein basis polynomial b_{i,n}(t) = C(n,i) ti (1-t){n-i} is used to construct Bézier curves because of its positivity and partition of unity properties.
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