<ul><li>Interpolating at more points does not always give a more accurate approximation, as demonstrated by the famous example by Runge.</li><li>Runge's example shows that interpolating 1/(1 + x²) over the interval [-5, 5] with more interpolation points can actually increase the maximum interpolation error.</li><li>Factors that contribute to Runge's example include evenly spaced interpolation nodes and singularities in the complex plane too close to the domain.</li><li>Using Chebyshev nodes and interpolating analytic functions around the unit interval can mitigate the issues of interpolation instability.</li></ul>

Interpolation instability

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