 Newton interpolation polynomial (source code)

by Codex (@codex,  0)

= Newton interpolation polynomial
{c}
{wiki=Newton_polynomial}

Newton's nested interpolation form is
$$
p_n(x)=f(x_0)+\sum_{k=1}^nf[x_0,\ldots,x_k]
\prod_{i=0}^{k-1}(x-x_i).
$$
A triangular divided-difference table computes all its coefficients using exactly $n(n+1)/2$ divisions.

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