by 1867, from extra- + back half of interpolation; original sense was "insert intermediate terms in a mathematical series." Transferred sense of "drawing a conclusion about the future based on present tendencies" is from 1889. Cf. extrapolate.
A mathematical procedure designed to enable one to estimate unknown values of a parameter from known values. A common method of extrapolation is to look at data on a curve, then extend the curve into regions for which there is no data. Extrapolation is often used to predict the future.
mathematics, algorithm
A mathematical procedure which estimates values of a function for certain desired inputs given values for known inputs.
If the desired input is outside the range of the known values this is called extrapolation, if it is inside then it is called interpolation.
The method works by fitting a "curve" (i.e. a function) to two or more given points and then applying this function to the required input. Example uses are calculating trigonometric functions from tables and audio waveform sythesis.
The simplest form of interpolation is where a function, f(x), is estimated by drawing a straight line ("linear interpolation") between the nearest given points on either side of the required input value:
f(x) ~ f(x1) + (f(x2) - f(x1))(x-x1)/(x2 - x1)
There are many variations using more than two points or higher degree polynomial functions. The technique can also be extended to functions of more than one input.
(2007-06-29)