Richardson extrapolation
Sequence acceleration method in numerical analysis / From Wikipedia, the free encyclopedia
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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 for several values of , we can estimate by extrapolating the estimates to . It is named after Lewis Fry Richardson, who introduced the technique in the early 20th century,[1][2] though the idea was already known to Christiaan Huygens in his calculation of .[3] In the words of Birkhoff and Rota, "its usefulness for practical computations can hardly be overestimated."[4]
Practical applications of Richardson extrapolation include Romberg integration, which applies Richardson extrapolation to the trapezoid rule, and the Bulirsch–Stoer algorithm for solving ordinary differential equations.