Chebyshev Nodes

Updated 01 Oct 2026

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What it is
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  interpolation nodes clustered toward the endpoints of an interval
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Formula
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  on $-1,1$ , $x_j=\cos((2j+1)\pi/[2(n+1)])$ , for $j=0,\ldots,n$ .
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  map these affinely to another interval.
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Purpose
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  reduce the maximum magnitude of the nodal product appearing in the interpolation error bound
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Caution
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  this property does not mean the resulting interpolant is the best minimax approximation to every funciton
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Related
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  Runge's Phenomenon,
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  Polynomial Interpolation
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Linked references 2