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 ?
And we observed that it is useful to perform some iterations before applying vector extrapolation methods in practice.
Sadok, "Vector extrapolation methods. Applications and numerical comparison," Journal of Computational and Applied Mathematics, vol.
A sufficient condition is that the extrapolation method does not depend on [lambda] so
The computational grid, the discretization of the body surface, and the extrapolation method used in these schemes are fully discussed.
To estimate the distribution of deforestation within each block, a second extrapolation method was adopted according to the relationship between the TM and MODIS deforestations derived from the sample blocks as in Hansen et al.
REDIVO ZAGLIA, Extrapolation Methods. Theory and Practice, North-Holland, Amsterdam, 1991.
The Standard Extrapolation Method, model Q1 (19), here denoted SEM-Q1, uses a standard three-adjustable parameter model (Eq 6), and expected failure times are calculated using a statistical approach.
The revised proxy was derived utilizing the average of the original loss curve and pool factor extrapolation methods. Based on the current credit enhancement and 6.00% loss proxy, the securities are able to withstand stress scenarios consistent with the ratings stated above, and make full payments to investors in accordance with the terms of the documents.
In Section 3, we introduce polynomial extrapolation methods. Numerical examples are reported in Section 4.
Based on transaction performance to date, Fitch utilized the average of the straight-line and pool factor loss extrapolation methods to arrive at a lifetime CNL proxy of 0.40% for this review.
A typical approach to reduce truncation artifacts is to perform extrapolation, for example, with the symmetric mirroring method [1], water cylinder extrapolation method [2], optimization-based extrapolation scheme [3], or implicit extrapolation method performed in the second-order derivative domain [4].

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