extrapolation
NounOpen English WordNet
Noun (2)
- (mathematics) calculation of the value of a function outside the range of known valuesType of calculation, computation
- an inference about the future (or about some hypothetical situation) based on known facts and observationsType of inference, illationKinds trend extrapolation
What does it mean? Question 1 of today’s quiz
Free On-line Dictionary of Computing
<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)