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:
“Buddhists and Christians contrive to agree about death
Making death their ideal basis for different ideals.
The Communists however disapprove of death
Except when practical.”
—William Empson (1906–1984)
“... the function of art is to do more than tell it like it is—it’s to imagine what is possible.”
—bell hooks (b. c. 1955)