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  "body": "\n## Summary\n\nMany linear approximation methods cannot converge faster than a certain rate, except for a small class of trivial functions.\nThis phenomenon is called saturation, and that rate is the saturation order of the method.\nThe functions approximated with exactly this rate form the saturation class.\nSaturation explains why smoothness beyond a certain level does not improve methods such as Bernstein polynomials or Fejér means.\n\n## Explanations\n\n### L1 human\n\nSome approximation methods hit a speed limit.\nBernstein polynomials of a function with a nonzero second derivative have error of order $1/n$ and not smaller, however smooth the function is.\nOnly the straight lines, which the method reproduces exactly, do better.\nKnowing the speed limit of a method tells when it is worth switching to a better one.\n",
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