SIAM Review, Volume 62, Issue 1, Page 231-243, January 2020.
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.

中文翻译：

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Runge插值示例和Wilkinson寻根示例

SIAM评论，第62卷，第1期，第231-243页，2020年1月。
我们看一下数值分析理论中的两个经典示例，即用于插值的Runge示例和用于求根的Wilkinson示例（实际上是两个示例）。我们使用威尔金森（Wilkinson）倡导和推广的现代后向误差分析和条件理论，但Farouki和Rajan对其进行了完善。通过这种方式，当学生尝试将多项式拟合到数值数据时，或者当他们尝试使用数字根查找来找到多项式零时，我们对学生所遇到的令人困惑的现象给出了令人满意的解释。计算机代数以其可控制的任意精度发挥着重要的教学作用。