Function approximation: Difference between revisions
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A function approximation problem asks us to select a function among a well-defined class that closely matches (approximates) a target function. | A function approximation problem asks us to select a function among a well-defined class that closely matches (approximates) a target function. | ||
There are two major classes of function approximation problems. For known target functions approximation theory investigates how certain known functions can be approximated by a specific class of functions (for example, polynomials or rational functions). | There are two major classes of function approximation problems. For known target functions approximation theory investigates how certain known functions can be approximated by a specific class of functions (for example, polynomials or rational functions). | ||
In the second class of problems, the target function (say ''f'') may be unknown. Instead of an explicit formula, only a set of points of the form (''x'', '' | In the second class of problems, the target function (say ''f'') may be unknown. Instead of an explicit formula, only a set of points of the form (''x'', ''f''(''x'')) is provided. Several techniques for approximating ''f'' may be applicable (depending on the structure of the [[domain]] and [[codomain]] of ''f''), such as [[interpolation]], [[extrapolation]], [[regression analysis]], and [[curve fitting]]. | ||
== See also == | |||
*[[Approximation theory]] | |||
*[[Least squares approximation]] | |||
*[[Moving least squares]] | |||
*[[Function (mathematics)]] | |||
*[[Regression analysis]] | |||
Latest revision as of 19:21, 17 January 2008
A function approximation problem asks us to select a function among a well-defined class that closely matches (approximates) a target function.
There are two major classes of function approximation problems. For known target functions approximation theory investigates how certain known functions can be approximated by a specific class of functions (for example, polynomials or rational functions).
In the second class of problems, the target function (say f) may be unknown. Instead of an explicit formula, only a set of points of the form (x, f(x)) is provided. Several techniques for approximating f may be applicable (depending on the structure of the domain and codomain of f), such as interpolation, extrapolation, regression analysis, and curve fitting.