Fundamental Methods of Extrapolation Fundamental Methods of Numerical Extrapolation With Applications

Extrapolation is an incredibly powerful technique for increasing speed and accuracy in various numerical tasks in scientific computing. As we will see, extrapolation can transform even the most mundane of algorithms (such as the Trapezoid Rule) into an extremely fast and accurate algorithm, increasing the rate of convergence by more than one order of magnitude. Within this paper, we will first present some background theory to motivate the derivation of Richardson and Romberg Extrapolation and provide support for their validity and stability as numerical techniques. Then we will present examples from differentiation and integration to demonstrate the incredible power of extrapolation. We will also give some MATLAB code to show some simple implentation methods in addition to discussing error bounds and differentiating between ”‘true”’ and ”‘false”’ convergence.