“Basis function”的意思、由来-开放百科全书

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Basis function

释义

Examples
Polynomial bases Fourier basis
References
See also
References

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).

Examples

Polynomial bases

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

Fourier basis

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).

References

{{cite book |last=Ito |first=Kiyoshi |authorlink= |coauthors= |others= |title=Encyclopedic Dictionary of Mathematics |edition=2nd |year=1993 |publisher=MIT Press |location= |isbn=0-262-59020-4 | page=1141}}

References

1. ^{{Cite journal|date=2007-08-01|title=Solutions of differential equations in a Bernstein polynomial basis|url=https://www.sciencedirect.com/science/article/pii/S0377042706003153|journal=Journal of Computational and Applied Mathematics|language=en|volume=205|issue=1|pages=272–280|doi=10.1016/j.cam.2006.05.002|issn=0377-0427}}

5 : Numerical analysis|Fourier analysis|Linear algebra|Numerical linear algebra|Types of functions

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Examples

Polynomial bases

Fourier basis

References

See also

References