Editing Interpolation (section)

{{Short description|Method for estimating new data within known data points}}
{{Other uses}}
{{distinguish|Interpellation (disambiguation){{!}}Interpellation}}

{{more footnotes|date=October 2016}}
In the [[mathematics|mathematical]] field of [[numerical analysis]], '''interpolation''' is a type of [[estimation]], a method of constructing (finding) new [[data points]] based on the range of a [[discrete set]] of known data points.<ref>{{cite EB1911 |wstitle=Interpolation |volume=14 |pages=706–710 |first=William Fleetwood |last=Sheppard |author-link=William Fleetwood Sheppard}}</ref><ref>{{Cite book|last=Steffensen|first=J. F.|url=https://www.worldcat.org/oclc/867770894|title=Interpolation|date=2006|isbn=978-0-486-15483-1|edition=Second|location=Mineola, N.Y.|oclc=867770894}}</ref>

In [[engineering]] and [[science]], one often has a number of data points, obtained by [[sampling (statistics)|sampling]] or [[experimentation]], which represent the values of a function for a limited number of values of the [[Dependent and independent variables|independent variable]]. It is often required to '''interpolate'''; that is, estimate the value of that function for an intermediate value of the independent variable.

A closely related problem is the [[function approximation|approximation]] of a complicated function by a simple function. Suppose the formula for some given function is known, but too complicated to evaluate efficiently. A few data points from the original function can be interpolated to produce a simpler function which is still fairly close to the original. The resulting gain in simplicity may outweigh the loss from interpolation error and give better performance in calculation process.

[[File:Splined epitrochoid.svg|300px|thumb|An interpolation of a finite set of points on an [[epitrochoid]]. The points in red are connected by blue interpolated [[spline (mathematics)|spline curves]] deduced only from the red points. The interpolated curves have polynomial formulas much simpler than that of the original epitrochoid curve.]]