Ékstrapolasi Richardson: Béda antarrépisi

Dina [[analisis numeris]], '''ékstrapolasi Richardson''' nyaéta métode [[akselerasi runtuyan]], nu digunakeun pikeun ngabebenah [[rarata konvergénsi]] tina [[runtuyan]]. Dingaranan sanggeus kapanggih ku [[Lewis Fry Richardson]], nu manggihan téhnik ieu dina mangsa awal [[abad ka-20]].

 

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Suppose that ''A''(''h'') is an estimation of order ''hⁿ'' for

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).

 

Let ''A''(''h'') be an approximation of ''A'' that depends on a positive step size ''h'' with an [[Approximation error|error]] formula of the form

:<math> A - A(h) = a_0h^{k_0} + a_1h^{k_1} + a_2h^{k_2} + \cdots </math>

It should be noted that the Richardson extrapolation can be considered as a linear [[sequence transformation]].

 

 

Using [[Taylor's theorem]],

:<math> A = \frac{4A_1\left(\frac{h}{2}\right) - A_1(h)}{3} + O(h^3) .</math>

 

 

*''Extrapolation Methods. Theory and Practice'' ku C. Brezinski jeung M. Redivo Zaglia, North-Holland, 1991.

 

* [[Aitken's delta-squared process]]

* [http://www.google.com/search?q=Richardson+extrapolation Nyungsi 'Richardson extrapolation' di google]

 

 

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