The Runge Example for Interpolation and Wilkinson's Examples for Rootfinding
Abstract
We look at two classical examples in the theory of numerical analysis, namely, the Runge example for interpolation and Wilkinson's example (actually two examples) for rootfinding. We use the modern theory of backward error analysis and conditioning, as instigated and popularized by Wilkinson but refined by Farouki and Rajan. By this means, we arrive at a satisfactory explanation of the puzzling phenomena encountered by students when they try to fit polynomials to numerical data, or when they try to use numerical rootfinding to find polynomial zeros. Computer algebra, with its controlled, arbitrary precision, plays an important didactic role.
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© 2020, Society for Industrial and Applied Mathematics.
History
Submitted: 17 January 2018
Accepted: 7 February 2019
Published online: 11 February 2020
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