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Student[NumericalAnalysis]

 NevilleTable
 compute the Neville table of an interpolation structure

 Calling Sequence NevilleTable(p) NevilleTable(p, pt)

Parameters

 p - a POLYINTERP structure pt - (optional) numeric, name; a point to evaluate the Neville table at or a name to assign to the independent variable in the Neville table

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{NumericalAnalysis}\right]\right):$
 > $\mathrm{xy}≔\left[\left[1.0,0.7651977\right],\left[1.3,0.6200860\right],\left[1.6,0.4554022\right],\left[1.9,0.2818186\right]\right]$
 ${\mathrm{xy}}{≔}\left[\left[{1.0}{,}{0.7651977}\right]{,}\left[{1.3}{,}{0.6200860}\right]{,}\left[{1.6}{,}{0.4554022}\right]{,}\left[{1.9}{,}{0.2818186}\right]\right]$ (1)
 > $\mathrm{p1}≔\mathrm{PolynomialInterpolation}\left(\mathrm{xy},\mathrm{method}=\mathrm{neville},\mathrm{extrapolate}=\left[1.5\right]\right):$
 > $\mathrm{NevilleTable}\left(\mathrm{p1},1.5\right)$
 $\left[\begin{array}{cccc}{0.7651977}& {0}& {0}& {0}\\ {0.6200860}& {0.5233448671}& {0}& {0}\\ {0.4554022}& {0.5102968002}& {0.5124714781}& {0}\\ {0.2818186}& {0.5132634002}& {0.5112856669}& {0.5118126939}\end{array}\right]$ (2)
 > $\mathrm{NevilleTable}\left(\mathrm{p1},1.8\right)$
 $\left[\begin{array}{cccc}{0.7651977}& {0}& {0}& {0}\\ {0.6200860}& {0.3782331671}& {0}& {0}\\ {0.4554022}& {0.3456130002}& {0.3347396114}& {0}\\ {0.2818186}& {0.339679800}& {0.3406686668}& {0.3400098828}\end{array}\right]$ (3)