Civil and Environmental Engineering 2219A/B Lecture Notes - Lecture 28: Richardson Extrapolation, Numerical Integration
5 May 2019
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Document Summary
The methods we will see today will help us to efficiently increase the accuracy. Richardson provides an accurate integral estimate by combining two less accurate integral estimates (richardson = trapz) Gauss quadrature provides superior integral estimates by picking optimal x-values at which to evaluate the function. Adaptive quadrature provides an accurate integral estimate (higher-order polynomial in a. Simpson estimate) by combining two less accurate integral estimates (adaptive = lower- order polynomial simpson estimate) Recall functions can be integrated in two forms: Richardson extrapolation methods use two estimates of an integral to compute a third, more accurate approximation. The two integral estimates ( 1) ( 2) are based on a trapezoidal rule using step sizes. Then the improved estimate of the integral is represented as: She was like "lol nope you don"t need to know this" For the special case where the interval is halved ( 2= 1 / 2 ), this becomes:
