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:
“My dream is that as the years go by and the world knows more and more of America, it ... will turn to America for those moral inspirations that lie at the basis of all freedom ... that America will come into the full light of the day when all shall know that she puts human rights above all other rights, and that her flag is the flag not only of America but of humanity.”
—Woodrow Wilson (1856–1924)
“Every boy was supposed to come into the world equipped with a father whose prime function was to be our father and show us how to be men. He can escape us, but we can never escape him. Present or absent, dead or alive, real or imagined, our father is the main man in our masculinity.”
—Frank Pittman (20th century)