“extrapolation”的概念、定义、翻译、参考文献-科学参考

extrapolation

Physics

An approximation technique for finding the value of a function or measurement beyond the values already known. If the values f(x₀), f(x₁),…,f(x_n) of a function of a variable x are known in the interval [x₀,x_n], the value of f(x) for a value of x outside the interval [x₀,x_n] can be found by extrapolation. The techniques used in extrapolation are usually not as good as those used in interpolation.

Mathematics

Suppose that certain values f(x₀), f(x₁),…, f(x_n) of a function f are known, where $x_{0} < x_{1} < \dots < x_{n}$ . A method of finding from these an approximation for f(x), for a given value of x that lies outside the interval [x₀, x_n], is called extrapolation. Such methods are normally far less reliable than interpolation, in which x lies between x₀ and x_n.

Statistics

The use of a formula, deduced from an initial set of data, for data values outside the range of the initial data set. Compare interpolation. Excessive extrapolation may give unreliable values and is not recommended.
For example, if we discover that 1 kg of fertilizer per ha results in a yield of 50 kg of produce per ha, that 1.5 kg gives 60 kg, and that 2 kg gives 70 kg, then we might reasonably extrapolate that 2.5 kg would give 80 kg. However, it would be excessive extrapolation to expect 10 kg to give 230 kg.

Chemical Engineering

A method of obtaining data that falls outside a range of known data that assumes the estimated data can be obtained by extending the known data.

Computer

The estimation of the value of a function (given other values of the function) at a point beyond the interval in which the data lies. One possible approach is to use the value of an interpolation polynomial at this point. An important case arises when the data consists of approximations to the solution of a problem, for different values of a parameter controlling the magnitude of the acceptable error in the method used. A more powerful method can be constructed by extrapolating to the limiting case of the parameter, where the error is zero, using theoretical results giving the dependence of the error on the parameter. This is called Richardson extrapolation (or the deferred approach to the limit).

Economics

Construction of new data points outside the given set of existing data points. Popular methods are linear and polynomial extrapolation; linear extrapolation uses regression-like techniques and is similar to linear prediction. The reliability of extrapolation is measured by the prediction error or the prediction confidence interval.

单词	extrapolation
释义	extrapolation Physics An approximation technique for finding the value of a function or measurement beyond the values already known. If the values f(x₀), f(x₁),…,f(x_n) of a function of a variable x are known in the interval [x₀,x_n], the value of f(x) for a value of x outside the interval [x₀,x_n] can be found by extrapolation. The techniques used in extrapolation are usually not as good as those used in interpolation. Mathematics Suppose that certain values f(x₀), f(x₁),…, f(x_n) of a function f are known, where $x_{0} < x_{1} < \dots < x_{n}$ . A method of finding from these an approximation for f(x), for a given value of x that lies outside the interval [x₀, x_n], is called extrapolation. Such methods are normally far less reliable than interpolation, in which x lies between x₀ and x_n. Statistics The use of a formula, deduced from an initial set of data, for data values outside the range of the initial data set. Compare interpolation. Excessive extrapolation may give unreliable values and is not recommended. For example, if we discover that 1 kg of fertilizer per ha results in a yield of 50 kg of produce per ha, that 1.5 kg gives 60 kg, and that 2 kg gives 70 kg, then we might reasonably extrapolate that 2.5 kg would give 80 kg. However, it would be excessive extrapolation to expect 10 kg to give 230 kg. Chemical Engineering A method of obtaining data that falls outside a range of known data that assumes the estimated data can be obtained by extending the known data. Computer The estimation of the value of a function (given other values of the function) at a point beyond the interval in which the data lies. One possible approach is to use the value of an interpolation polynomial at this point. An important case arises when the data consists of approximations to the solution of a problem, for different values of a parameter controlling the magnitude of the acceptable error in the method used. A more powerful method can be constructed by extrapolating to the limiting case of the parameter, where the error is zero, using theoretical results giving the dependence of the error on the parameter. This is called Richardson extrapolation (or the deferred approach to the limit). Economics Construction of new data points outside the given set of existing data points. Popular methods are linear and polynomial extrapolation; linear extrapolation uses regression-like techniques and is similar to linear prediction. The reliability of extrapolation is measured by the prediction error or the prediction confidence interval.
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