Topic
functional for polynomials
In numerical analysis, a blossom is a functional that can be applied to any polynomial, but is mostly used for Bézier and spline curves and surfaces.
“Flowers are the sweetest things that God ever made, and forgot to put a soul into.”
“Where flowers degenerate man cannot live.”
“Just then return'd at shut of evening flowers.”
“The flower of sweetest smell is shy and lowly.”
“And wild-scatter'd cowslips bedeck the green dale.”
“Her heart was a passion-flower, bearing within it the crown of thorns and the cross of Christ.”
Quotes via Wikiquote (CC BY-SA), each with its original source.
Not who you're looking for? Others named blossom: protagonist of The Powerpuff Girls · American television series · 2016 song by Kerli · British brig
In numerical analysis, a blossom is a functional that can be applied to any polynomial, but is mostly used for Bézier and spline curves and surfaces.
The blossom of a polynomial ƒ, often denoted
B
[
f
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{\displaystyle {\mathcal {B}}[f],}
is completely characterised by the three properties:
It is a symmetric function of its arguments:
B
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u
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=
B
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π
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,
{\displaystyle {\mathcal {B}}[f](u_{1},\dots ,u_{d})={\mathcal {B}}[f]{\big (}\pi (u_{1},\dots ,u_{d}){\big )},\,}
(where π is any permutation of its arguments).
It is affine in each of its arguments:
B
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α
u
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β
v
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=
α
B
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B
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when
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1.
{\displaystyle {\mathcal {B}}[f](\alpha u+\beta v,\dots )=\alpha {\mathcal {B}}[f](u,\dots )+\beta {\mathcal {B}}[f](v,\dots ),{\text{ when }}\alpha +\beta =1.\,}
It satisfies the diagonal property:
B
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u
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=
f
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{\displaystyle {\mathcal {B}}[f](u,\dots ,u)=f(u).\,}
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