Table 1 Neville table built from q initial approximations Y T τ ₁ ,…, Y T τ _q with order k ₁ (first column) and extrapolated to find a solution of order k _q , that is $Y_T^{{\tau }_1,{\tau }_q}$

${\mathbf{Y}}_T^{{\tau }_1}$

${\mathbf{Y}}_T^{{\tau }_1,{\tau }_2}$

Approximate

${\mathbf{Y}}_T^{{\tau }_2}$

${\mathbf{Y}}_T^{{\tau }_1,{\tau }_3}$

solutions

${\mathbf{Y}}_T^{{\tau }_2,{\tau }_3}$

⋮

$\dots {\mathbf{Y}}_T^{{\tau }_1,{\tau }_q}$

${\mathbf{Y}}_T^{{\tau }_3}$

⋮

${\mathbf{Y}}_T^{{\tau }_{q-2},{\tau }_q}$

⋮

${\mathbf{Y}}_T^{{\tau }_{q-1},{\tau }_q}$

${\mathbf{Y}}_T^{{\tau }_q}$