= Chebyshev minimax polynomial with exterior normalization
{c}
{title2=$p_k(t)=T_k(z(t))/T_k(z(0)),\quad z(t)=(2t-a-b)/(b-a)$}
For $0<a<b$, the displayed polynomial minimizes $\max_{t\in[a,b]}|p(t)|$ among real polynomials of degree at most $k$ with $p(0)=1$. Its $k+1$ alternating extremal values prove the assertion: a strictly smaller competitor would make the difference change sign in each consecutive extremal interval and also vanish at zero outside $[a,b]$, giving too many roots. The normalizing factor makes either the monic or the usual <Chebyshev polynomial> convention give the same ratio. For $\kappa=b/a$ and $q=(\sqrt\kappa-1)/(\sqrt\kappa+1)$, its maximum is $2q^k/(1+q^{2k})$. This yields an error bound for polynomial acceleration of <Richardson iteration>.
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