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  "body": "\n## Summary\n\nThe Remez algorithm is an iterative method that computes the [[minimax approximation|ASWF03X5AM]] of a continuous function by polynomials of a given degree.\nEach round has two steps.\nFirst it fits a polynomial whose error has equal size and alternating signs on $n + 2$ reference points.\nThen it moves the reference points to the places where the error is largest.\nIt was introduced by Evgeny Remez in 1934 and is a standard way to design polynomial and rational approximations in numerical libraries.\n\n## Explanations\n\n### L1 human\n\nThe best uniform approximation has an error curve that wiggles up and down with equal height at $n + 2$ places.\nThe algorithm guesses those places, forces the error to have equal height there, and then looks where the error is really largest.\nIt moves the guessed places there and repeats.\nFor a straight-line approximation of $x^2$ on $[-1, 1]$, starting from the points $-1, 0, 1$ already gives the answer $1/2$ in one step.\n",
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