extrapolation


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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 ?
Adopting commonly accepted testing, extrapolation analysis, materials and processes will help manufacturers achieve proven quality, reliability and consistency while also helping suppliers focus on a single set of criteria (instead of having to meet different requirements for each customer).
In addition, EMA is finalising a reflection paper which outlines a systematic approach to scientifically sound and reliable extrapolation of data to support medicine authorisation.
In this paper the combination of the Richardson extrapolation [15] with different numerical methods is studied to determine its advantages respect to tradditional methods, such as the trapezoidal integration commonly used in power system dynamic equations [16].
Steel's focus in Across the Boundaries is to deal with the methodological problems associated with making extrapolations in the social sciences via a comparison with the manner in which extrapolation works in the biological sciences.
For nonlinear extrapolation resulting in a RfD (which the U.
The matrices inside and outside the sub-band are generated via interpolation and extrapolation, respectively.
1] proposed a new cascadic multi-grid method called new extrapolation cascadic multi-grid method, for solving elliptic PDEs.
For example, if an RAC finds a 10% error rate on 50 medical records, extrapolation would allow the contractor to apply that error rate across all of a physician's Medicare patients over multiple years--potentially dramatically increasing the penalty.
For example, if a RAC finds a 10% error rate on 50 medical records, extrapolation would allow the contractor to apply that error rate across all of a physician's Medicare patients over multiple years--potentially dramatically increasing the penalty.
I do not, however, understand the extrapolation he makes in Figure 4, where he summarizes and plots biopositive radiation effects on cancer mortality from several studies.
Extrapolation practice for ecotoxicological effect characterization of chemicals.
By relying on simple extrapolation, the new study has underestimated the immediacy of the threat, he says.