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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).

Contents

ExamplesEdit

Polynomial basesEdit

The base of a polynomial is the factored polynomial equation into a linear function.[1]

Fourier basisEdit

Sines and cosines form an (orthonormal) Schauder basis for square-integrable functions. As a particular example, the collection:

 

forms a basis for L2(0,1).

ReferencesEdit

  • Ito, Kiyoshi (1993). Encyclopedic Dictionary of Mathematics (2nd ed.). MIT Press. p. 1141. ISBN 0-262-59020-4. 

See alsoEdit

ReferencesEdit

  1. ^ "Solutions of differential equations in a Bernstein polynomial basis". Journal of Computational and Applied Mathematics. 205 (1): 272–280. 2007-08-01. doi:10.1016/j.cam.2006.05.002. ISSN 0377-0427.