extrapolation

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Related to Linear extrapolation: Linear interpolation

extrapolation

[ik‚strap·ə′lā·shən]
(mathematics)
Estimating a function at a point which is larger than (or smaller than) all the points at which the value of the function is known.

Extrapolation

 

in mathematics and statistics, the approximate determination of the values of a function f(x) at points x lying outside the interval [x0, xn] on the basis of the function’s values at the points x0 < x1 <... < xn In parabolic extrapolation, which is the most widely encountered type, the value of f(x) at x is approximated by the value of a polynomial Pn(x ) of degree n that assumes at the n + 1 points xi the specified values yi = f (xi). Interpolation formulas are used for parabolic extrapolation.

extrapolation

(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.
References in periodicals archive ?
Obviously, linear extrapolation is not conservative at all if it is actually the correct model for the substance at issue; even if the U.
The error in the linear extrapolation results is rather negligible in comparison with those associated with the other methods as the experimental temperatures are used directly and the spatial measurements are extremely close to the contact surface.
The first aim of the present study was to justify linear extrapolation of P/log D plots to P = 0.
Thus it was no longer reasonable to expect a simple linear extrapolation to give meaningful values of [w.
It is based primarily on a linear extrapolation of data from mines, because lower indoor concentrations make studies in homes inconclusive.
Bulgrin says one of Van Dorn's feed-forward filters looks ahead by "simple linear extrapolation.

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