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

(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.

This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)

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 It might be outdated or ideologically biased.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, x_n] on the basis of the function’s values at the points x₀ < x₁ <... < x_n 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 P_n(x ) of degree n that assumes at the n + 1 points x_i the specified values y_i = f (x_i). Interpolation formulas are used for parabolic extrapolation.

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References in periodicals archive

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.

The use of biosimilar medicines in oncology--position statement of the Brazilian Society of Clinical Oncology (SBOC)

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.

BECQUER'S EXTRAPOLATION TO EXPRESS THE INEFFABLE

The work shows the viscometric relations of monomers (MBC) and its newly synthesized polythioamides by a single point determination and graphic extrapolation method.

Viscometric Study of Poly [4,4'-Methylenebis(cinnamalthioyl)diamine] and derived Polythioamides by (DSV) method

We also investigate the performance of the state-of-the-art water cylinder extrapolation method [2] and compare it with our proposed method.

An Improved Extrapolation Scheme for Truncated CT Data Using 2D Fourier-Based Helgason-Ludwig Consistency Conditions

Extrapolations from this paper are fairly straightforward.

Is MDx cost-effective for infectious disease applications?

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.

SI simulation quality relies on VNA measurement accuracy

The sections are arranged as follows: the fourth order compact difference scheme and Richardson extrapolation technique are given in Section 2.

Richardson cascadic multigrid method for 2D poisson equation based on a fourth order compact scheme

She says extrapolations that are typically used in Medicaid audits have been quite a source of interest lately for providers and rule makers.

Verifying an audit's accuracy: when faced with a Medicaid audit, providers may question the audit's methodology and results as the basis for a legal appeal