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basis function

(one of a set of functions used to approximate a function of interest)

The term basis function is used for function selected to help describe a function or relation of interest (to specify it exactly or to approximate it); one might (often roughly) specify the relation-of-interest by a parameterized combination of such basis functions. Modeling, such as through numerical approximations of partial differential equations (PDEs), can be organized through the use of basis functions, parameterized and combined (e.g., summed) to approximate a function of interest. An example is the sine function, as used to form a Fourier series. The concept is also used in the finite element method and similar methods of solving PDEs.


The term basis function is also used regarding models, e.g., statistical analysis or machine learning. There are well-known techniques to find a good fit when a relationship is linear, but for data without such a simple relation, some particular function (e.g., square, polynomial of some degree, exponential) may fit, such as a case where you can find the fit if you assume the data fits a square relation. The term basis function is used for such functions you specify. In some cases, it is possible to reduce trials by trying a linear combination of such functions simultaneously, which reveals one or a combination that fits well. Some phenomena you model will have an inherent function that will fit if you know to try it, but also there are very flexible types of functions that would not be termed inherent, but can be the basis for useful heuristic models.


(mathematics,computation)
Further reading:
https://en.wikipedia.org/wiki/Basis_function
https://www.statisticshowto.com/basis-functions-simple-definition/
https://www.psych.mcgill.ca/misc/fda/ex-basis-a1.html
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Quantum_States_of_Atoms_and_Molecules_(Zielinksi_et_al)/10%3A_Theories_of_Electronic_Molecular_Structure/10.03%3A_Basis_Functions

Referenced by page:
Bernstein polynomial

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