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Richardson’s extrapolation spreadsheet calculator has been developed to approximate the derivative of the given function at a chosen point with a step size h . The Excel commands that calculate Richardson’s extrapolation values are given in Table 1 and the layout of the spreadsheet calculator is shown in Figure 1.What is the difference between interpolation and Richardson extrapolation?
Interpolation is to estimate a value between a given set of known values. Extrapolation is touse known values to project a value outside of the intended range of the previous values. Using theconcept of Richardson Extrapolation, very higher order integration can be achieved using only aseries of values from Trapezoidal Rule.Can Richardson extrapolation be considered as a linear sequence transformation?
The Richardson extrapolation can be considered as a linear sequence transformation . Additionally, the general formula can be used to estimate k0 (leading order step size behavior of Truncation error) when neither its value nor A* (exact value) is known a priori. Such a technique can be useful for quantifying an unknown rate of convergence.What is the best extrapolation for a trapezoidal rule?
Using Richarson Extrapolation, the best value can be extrapolated to be. A0 = Ah + 1 (2n −1) (Ah −A2h) . Richardson Extrapolation for Trapezoidal Rule. With an order term of O(h2), the extrapolation for a better solution is. A0 = Ah + 1 3 (Ah −A2h) .