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MCS 471 Runge's Counter Example Against Using High Degree Polynomial Fits

Runge's example is

**R(x) = 1/(1+25*x^2), on [-1, +1],
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behaves like a polynmial,

**R(x) = 1 - 25*x^2 + O(x^4)**,

near the center **x = 0**, but behaves like a quadratic hyperbola,
**R(x) = 1/(25*x^2) + O(1/(25*x^2)^2)**,

near the endpoints **|x| = 1**.
Thus, a polynomial fit will have difficulty near the endpoints, where
the behavior is certainly not polynomial-like.

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Web Source: http://www.math.uic.edu/~hanson/mcs471/runge_example.html
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