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In mathematics, extrapolation is a type of estimation, beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to interpolation , which produces estimates between known observations, but extrapolation is subject to greater uncertainty and a higher risk of producing ...
Prediction outside this range of the data is known as extrapolation. Performing extrapolation relies strongly on the regression assumptions. The further the extrapolation goes outside the data, the more room there is for the model to fail due to differences between the assumptions and the sample data or the true values.
The term extrapolation is used to find data points outside the range of known data points. In curve fitting problems, the constraint that the interpolant has to go exactly through the data points is relaxed. It is only required to approach the data points as closely as possible (within some other constraints).
The original use of interpolation polynomials was to approximate values of important transcendental functions such as natural logarithm and trigonometric functions.Starting with a few accurately computed data points, the corresponding interpolation polynomial will approximate the function at an arbitrary nearby point.
In numerical analysis, Richardson extrapolation is a sequence acceleration method used to improve the rate of convergence of a sequence of estimates of some value = (). In essence, given the value of A ( h ) {\displaystyle A(h)} for several values of h {\displaystyle h} , we can estimate A ∗ {\displaystyle A^{\ast }} by extrapolating the ...
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In the synthetic track, methods were compared according to five properties: re-discovery of exact expressions; feature selection; resistance to local optima; extrapolation; and sensitivity to noise. Rankings of the methods were: QLattice; PySR (Python Symbolic Regression) uDSR (Deep Symbolic Optimization)
A famous example of extrapolation of static analysis comes from overpopulation theory. Starting with Thomas Malthus at the end of the 18th century, various commentators have projected some short-term population growth trend for years into the future, resulting in the prediction that there would be disastrous overpopulation within a generation or two.