Basis function
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.Examples
The base of a polynomial is the factored polynomial equation into a linear function.Fourier basis
Sines and cosines form an Schauder basis for square-integrable functions. As a particular example, the collection:
forms a basis for L2.
