# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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 ?
Traditional linear extrapolation employed in [14, 15] is based on the assumption that the hands always maintain uniform linear motion on both x and y coordinates between neighboring states.
Although the underlying mechanism responsible for the particle size distribution which gives rise to linear segments is not known, linear extrapolation to P = 0 covers a size range which it is difficult to actually measure.
In so mastering time, technology presents us with a future that is entirely known, predictable, and closed, an infinite and linear extrapolation of existing trends and technical capacities.
The linear extrapolation used represents a worst-case analysis of the expected aging by the oscillator.
Above the highest bid amount used, a linear extrapolation is made based on the proportion of "no" responses at the highest two bid levels.
Bulgrin says one of Van Dorn's feed-forward filters looks ahead by "simple linear extrapolation."
If there is no more plausible method of using rodent tests than the one employed under present science policy(12) (linear extrapolation to humans from testing at high doses), yet there is a strong political demand that government screen out risks in advance of epidemiological evidence (in other words, before mortality and disease occur), then even the best institutions will not produce a remedy.
If linear extrapolation had been substituted, the average absolute value of the projection error would have been slightly higher-7.15 percent of the 1980 baseline levels of employment.
Exposure limits for carcinogens that are genotoxic or without an established nongenotoxic MOA are usually based on other approaches, in particular the linear extrapolation approach (EFSA 2005; U.S.
Because of the sizeable approximations, this linear extrapolation is valid only at very small undercoolings (22).
PRE = Average error of linear extrapolation - Average error of real projection/Average error of real projection 100

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