= Gauss collocation coefficient construction
{c}
{title2=$a_{ij}=\int_0^{c_i}\ell_j(t)dt$}
Choose $c_1,\ldots,c_s$ as the <polynomial roots> of $P_s(2c-1)$ in $(0,1)$, and form the <Lagrange interpolation polynomials> $\ell_j(t)=\prod_{m\ne j}(t-c_m)/(c_j-c_m)$. The <Gauss collocation method> has $a_{ij}=\int_0^{c_i}\ell_j(t)dt$ and $b_j=\int_0^1\ell_j(t)dt$. This gives explicit coefficient formulas after finding <polynomial roots>: if $\ell_j(t)=\sum_rd_{jr}t^r$, these <integrals> are $\sum_rd_{jr}c_i^{r+1}/(r+1)$ and $\sum_rd_{jr}/(r+1)$. <Gaussian quadrature> gives order $2s$.
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