The NevilleTable command computes the Neville table of an interpolation structure created using the Neville interpolation method.

The POLYINTERP structure is created using the PolynomialInterpolation command.

Only POLYINTERP structures that were created using the Neville interpolation method are valid to use with this command.

If the parameter pt is not specified, the general unevaluated Neville table will be returned with the independent variable from when the POLYINTERP structure was computed.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{NumericalAnalysis}\right]\right)\:$

$\mathrm{xy}≔\left[\left[1.0\,0.7651977\right]\,\left[1.3\,0.6200860\right]\,\left[1.6\,0.4554022\right]\,\left[1.9\,0.2818186\right]\right]$

$\mathrm{xy}≔\left[\left[1.0\,0.7651977\right]\,\left[1.3\,0.6200860\right]\,\left[1.6\,0.4554022\right]\,\left[1.9\,0.2818186\right]\right]$

$\mathrm{p1}≔\mathrm{PolynomialInterpolation}\left(\mathrm{xy}\,\mathrm{method}=\mathrm{neville}\,\mathrm{extrapolate}=\left[1.5\right]\right)\:$

$\mathrm{NevilleTable}\left(\mathrm{p1}\,1.5\right)$

$\left[\begin{array}{cccc}0.7651977& 0& 0& 0\\ 0.6200860& 0.5233448671& 0& 0\\ 0.4554022& 0.5102968002& 0.5124714781& 0\\ 0.2818186& 0.5132634002& 0.5112856669& 0.5118126939\end{array}\right]$

$\mathrm{NevilleTable}\left(\mathrm{p1}\,1.8\right)$

$\left[\begin{array}{cccc}0.7651977& 0& 0& 0\\ 0.6200860& 0.3782331671& 0& 0\\ 0.4554022& 0.3456130002& 0.3347396114& 0\\ 0.2818186& 0.339679800& 0.3406686668& 0.3400098828\end{array}\right]$