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  "body": "\n## Summary\n\nThe Lebesgue constant of a set of interpolation nodes measures how much [[polynomial interpolation|SS1YMS2NPC]] at these nodes can amplify errors.\nIt is the [[operator norm|06EKW1AKXF]] of the interpolation map on continuous functions with the uniform norm.\nIt compares the interpolation error with the error of best approximation, and it measures the sensitivity of interpolation to errors in the data.\nFor equally spaced nodes it grows exponentially with the degree, while for [[Chebyshev nodes|HYK8J56PSH]] it grows only like a logarithm.\n\n## Explanations\n\n### L1 human\n\nSuppose the data values at the nodes are each wrong by at most $\\varepsilon$.\nThe interpolating polynomial may then be wrong by up to $\\Lambda \\varepsilon$ somewhere, where $\\Lambda$ is the Lebesgue constant.\nFor the nodes $-1, 0, 1$ the constant is $5/4$, so the amplification is mild.\nFor $20$ equally spaced nodes it is already in the thousands, which is one cause of Runge's phenomenon.\n",
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