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 ?
Due to the uncertainty within this extrapolation method and the limited information available from the measured data, the estimation of the cumulative probability might not be accurate in the absolute sense.
The extrapolation method can be effective, particularly when the temperature is measured at points extremely close to the contact interface.
Corrosion rates of the investigated materials were calculated using the Tafel extrapolation method.
We applied a polynomial vector extrapolation method, namely reduced rank extrapolation (RRE), to the iterative method proposed by Lin  which computes the minimal positive solution of NARE as the minimal positive solution of a vector equation.
The stability and integrity of the coating of the different traps is the most important condition for validity of the size extrapolation method for the neutron lifetime measurement.
The direction of change was always correctly indicated for the current-dollar estimates, and it was correctly indicated at least 90 percent of the time for the real estimates using either the single-deflation method or the extrapolation method.
Therefore, we applied an extrapolation method to determine the contact line position.
Based on transaction-specific performance to date, Fitch utilized the straight-line loss extrapolation method to arrive at a lifetime CNL proxy of 0.
Contract notice: Biogenic solid fuels in industry, trade, services sector (ghd) - development and validation of an extrapolation method for the determination of fuel use for the years 2005 to 2020.
If the original sequence is divergent, the sequence transformation acts as an extrapolation method to the anti-limit s.
Besides, calculation of the [gamma]-values required for the energy extrapolation method depends on the UCN spectra.
A linear extrapolation method was chosen as an operational definition of the glass transition temperature for this study.

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