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Mathematics > Numerical Analysis

arXiv:1804.08561 (math)
[Submitted on 23 Apr 2018]

Title:The Runge Example for Interpolation and Wilkinson's Examples for Rootfinding

Authors:Robert M. Corless, Leili Rafiee Sevyeri
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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.
Subjects: Numerical Analysis (math.NA)
MSC classes: 97N40
Cite as: arXiv:1804.08561 [math.NA]
  (or arXiv:1804.08561v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1804.08561

Submission history

From: Leili Rafiee Sevyeri [view email]
[v1] Mon, 23 Apr 2018 16:54:36 UTC (646 KB)
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