Function approximation
In general, a function approximation problem asks us to select a function among a well-defined class that closely matches ("approximates") a target function in a task-specific way. The need for function approximations arises in many branches of applied mathematics, and computer science in particular, such as predicting the growth of microbes in microbiology. Function approximations are used where theoretical models are unavailable or hard to compute. One can distinguish two major classes of function approximation problems:
- Comment
- enIn general, a function approximation problem asks us to select a function among a well-defined class that closely matches ("approximates") a target function in a task-specific way. The need for function approximations arises in many branches of applied mathematics, and computer science in particular, such as predicting the growth of microbes in microbiology. Function approximations are used where theoretical models are unavailable or hard to compute. One can distinguish two major classes of function approximation problems:
- Date
- enJanuary 2022
- Depiction
- DifferentFrom
- Function fitting
- Has abstract
- enIn general, a function approximation problem asks us to select a function among a well-defined class that closely matches ("approximates") a target function in a task-specific way. The need for function approximations arises in many branches of applied mathematics, and computer science in particular, such as predicting the growth of microbes in microbiology. Function approximations are used where theoretical models are unavailable or hard to compute. One can distinguish two major classes of function approximation problems: First, for known target functions approximation theory is the branch of numerical analysis that investigates how certain known functions (for example, special functions) can be approximated by a specific class of functions (for example, polynomials or rational functions) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.). Second, the target function, call it g, may be unknown; instead of an explicit formula, only a set of points of the form (x, g(x)) is provided. Depending on the structure of the domain and codomain of g, several techniques for approximating g may be applicable. For example, if g is an operation on the real numbers, techniques of interpolation, extrapolation, regression analysis, and curve fitting can be used. If the codomain (range or target set) of g is a finite set, one is dealing with a classification problem instead. To some extent, the different problems (regression, classification, fitness approximation) have received a unified treatment in statistical learning theory, where they are viewed as supervised learning problems.
- Is primary topic of
- Function approximation
- Label
- enFunction approximation
- Link from a Wikipage to another Wikipage
- Applied mathematics
- Approximation theory
- Category:Regression analysis
- Category:Statistical approximations
- Codomain
- Computer science
- Curve fitting
- Domain of a function
- Extrapolation
- File:Regression pic gaussien dissymetrique bruite.svg
- File:Step function approximation.png
- Fitness approximation
- Function (mathematics)
- Interpolation
- Kriging
- Least squares (function approximation)
- Microbiology
- Numerical analysis
- Polynomial
- Radial basis function network
- Rational function
- Real number
- Regression analysis
- Special function
- Statistical classification
- Statistical learning theory
- Supervised learning
- Reason
- enFind a source that actually explicitly makes this kind of definition; this one doesn't quite do so
- SameAs
- 3At9g
- Aproksimacija funkcija
- Function approximation
- m.01xlxg
- Q3445816
- Апроксимация на функции
- Апроксимација функција
- Subject
- Category:Regression analysis
- Category:Statistical approximations
- Thumbnail
- WasDerivedFrom
- Function approximation?oldid=1066689981&ns=0
- WikiPageLength
- 5311
- Wikipage page ID
- 336897
- Wikipage revision ID
- 1066689981
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