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extrapolation 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).