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In
numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...
, a blossom is a
functional Functional may refer to: * Movements in architecture: ** Functionalism (architecture) ** Form follows function * Functional group, combination of atoms within molecules * Medical conditions without currently visible organic basis: ** Functional sy ...
that can be applied to any
polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...
, but is mostly used for Bézier and spline curves and surfaces. The blossom of a polynomial ''ƒ'', often denoted \mathcal is completely characterised by the three properties: * It is a symmetric function of its arguments: :: \mathcal u_1,\dots,u_d) = \mathcal big(\pi(u_1,\dots,u_d)\big),\, : (where ''π'' is any
permutation In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...
of its arguments). * It is affine in each of its arguments: :: \mathcal \alpha u + \beta v,\dots) = \alpha\mathcal u,\dots) + \beta\mathcal v,\dots),\text\alpha + \beta = 1.\, * It satisfies the diagonal property: :: \mathcal u,\dots,u) = f(u).\,


References

* * * Numerical analysis {{mathanalysis-stub