Example of Richardson Extrapolation
Suppose that is an estimation of order for, i.e. . Then
is called the Richardson extrapolation of A(h); it is an estimate of order hm for A, with m>n.
More generally, the factor 2 can be replaced by any other factor, as shown below.
Very often, it is much easier to obtain a given precision by using R(h) rather than A(h') with a much smaller h', which can cause problems due to limited precision (rounding errors) and/or due to the increasing number of calculations needed (see examples below).
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“There are men who think themselves too wise to be religious.”
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