In mathematics, a basis function is an element of a particular basis for a function space. Every continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.
In numerical analysis and approximation theory, basis functions are also called blending functions, because of their use in interpolation: In this application, a mixture of the basis functions provides an interpolating function (with the "blend" depending on the evaluation of the basis functions at the data points).
Famous quotes containing the words basis and/or function:
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““... The state’s one function is to give.
The bud must bloom till blowsy blown
Its petals loosen and are strown;
And that’s a fate it can’t evade
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—Robert Frost (1874–1963)