Basis Function: Difference between revisions
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=== 2015 === | === 2015 === | ||
* (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/basis_function Retrieved:2015-1-18. | * (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/basis_function Retrieved:2015-1-18. | ||
** In [[mathematics]], a '''basis function</B> is an element of a particular [[Basis (linear algebra)|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 [[mathematics]], a '''basis function</B> is an element of a particular [[Basis (linear algebra)|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]]. <P> In [[numerical analysis]] and [[approximation theory]], basis functions are also called '''blending functions,</B> 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 point]]s). | ||
=== 2009 === | === 2009 === | ||
Revision as of 03:28, 16 August 2021
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):
- See: Finite Element Algorithm, Basis (Linear Algebra), Linear Combination, Basis Vector, Interpolation.
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).
- 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.
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.