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 ?
If any empirical model prediction requires stepping outside the bounds of the training data in the original experimental feature space, is it possible to find a different feature space (from the pool of 736,281 artificial feature spaces) where the predicted point is not an extrapolation?
In addition, it is important that the biosimilar be characterized with respect to its extrapolation, safety, and interchangeability and this information should be communicated to both physicians and pharmacists.
It is in the three "exchange" or "barter" poems--those which contain the verb "diera"--that Becquer fully submits to the ineffable while, conversely, using extrapolation to reach it.
The work shows the viscometric relations of monomers (MBC) and its newly synthesized polythioamides by a single point determination and graphic extrapolation method.
We also investigate the performance of the state-of-the-art water cylinder extrapolation method [2] and compare it with our proposed method.
The stable convergence behavior of the vector extrapolation based Landweber method makes it easy to be terminated by the simplified discrepancy principle [[parallel]A[s.sub.n,k] - b[[parallel].sub.2] [less than or equal to] [v.sub.dp][[parallel][eta][parallel].sub.2].
Extrapolations from this paper are fairly straightforward.
The other four recommended indications represented extrapolations, based on the totality of biosimilar evidence presented at the meeting by both Celltrion staffers and consultants as well as analyses presented by FDA staff members.
DC extrapolation is important in these models as well.
The sections are arranged as follows: the fourth order compact difference scheme and Richardson extrapolation technique are given in Section 2.
She says extrapolations that are typically used in Medicaid audits have been quite a source of interest lately for providers and rule makers.