The ExactValue command computes the value(s) of the exact function at specified point(s) pts or at the extrapolated point(s) from the POLYINTERP structure, depending on whether pts is given or not.

The exact values are returned in a list of the form [[${\mathrm{point}}_i$, ${\mathrm{exact}}_i$], [...], ...], $i$ = $1..\mathrm{number}$ $\mathrm{of}$ $\mathrm{points}$.

If the ExactValue command is used on a POLYINTERP structure whose exact function was not originally specified, an exception will be raised.

The POLYINTERP structure is created using the PolynomialInterpolation command or the CubicSpline command.

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

$\mathrm{xy}≔\left[\left[0\,4.0\right]\,\left[0.5\,0\right]\,\left[1.0\,-2.0\right]\,\left[1.5\,0\right]\,\left[2.0\,1.0\right]\,\left[2.5\,0\right]\,\left[3.0\,-0.5\right]\right]$

$\mathrm{xy}≔\left[\left[0\,4.0\right]\,\left[0.5\,0\right]\,\left[1.0\,\mathrm{-2.0}\right]\,\left[1.5\,0\right]\,\left[2.0\,1.0\right]\,\left[2.5\,0\right]\,\left[3.0\,\mathrm{-0.5}\right]\right]$

$\mathrm{p1}≔\mathrm{PolynomialInterpolation}\left(\mathrm{xy}\,\mathrm{function}=2^{2-x}\cos \left(\mathrm{\pi }x\right)\,\mathrm{method}=\mathrm{lagrange}\,\mathrm{extrapolate}=\left[0.25\,0.75\,1.25\right]\,\mathrm{errorboundvar}='\mathrm{\xi }'\right)\:$

$\mathrm{ExactValue}\left(\mathrm{p1}\right)$

$\left[\left[0.25\,2.378414230\right]\,\left[0.75\,\mathrm{-1.681792830}\right]\,\left[1.25\,\mathrm{-1.189207114}\right]\right]$

$\mathrm{ExactValue}\left(\mathrm{p1}\,\left[0.5\,1.0\right]\right)$

$\left[\left[0.5\,\mathrm{-5.801199657}\times {10}^{\mathrm{-10}}\right]\,\left[1.0\,\mathrm{-2.}\right]\right]$