Basis Function

A Basis Function is an element of a basis for a function space.

• Context:
  • It can be represented as an Expanded Basis Function.
  • It can range from being a Fixed Basis Function to being an Adaptive Basis Function.
  • …
• Example(s):
  • a Linear Basis Function.
  • a Non-linear Basis Function.
  • a Radial Basis Function.
• See: Finite Element Algorithm, Basis (Linear Algebra), Linear Combination, Basis Vector, Interpolation.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/basis_function Retrieved:2015-1-18.
  • 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).

2009

• (Gentle, 2009) ⇒ James E. Gentle. (2009). “Computational Statistics." Springer. ISBN:978-0-387-98143-7
  • QUOTE: Another approach to function estimation is to represent the function of interest as a linear combination of basis functions, that is, to represent the function in a series expansion. The basis functions are generally chosen to be orthogonal over the domain of interest, and the observed data are used to estimate the coefficients in the series.

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