DividedDifferenceTable - Maple Help

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Student[NumericalAnalysis]

 DividedDifferenceTable
 compute the divided difference table

 Calling Sequence DividedDifferenceTable(p) DividedDifferenceTable(p, pt)

Parameters

 p - a POLYINTERP structure pt - (optional) numeric; a point to evaluate the divided difference table

Description

 • The DividedDifferenceTable command takes an interpolation structure and computes the associated divided difference table.
 • This command can only be used on interpolation structures that were computed with Hermite or Newton methods.
 • The POLYINTERP structure is created using the PolynomialInterpolation command.

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)
 > $\mathrm{p1}≔\mathrm{PolynomialInterpolation}\left(\mathrm{xy},\mathrm{independentvar}='x',\mathrm{method}=\mathrm{newton}\right):$
 > $\mathrm{DividedDifferenceTable}\left(\mathrm{p1}\right)$
 $\left[\begin{array}{cccc}{0.7651977}& {0}& {0}& {0}\\ {0.6200860}& {-0.4837056667}& {0}& {0}\\ {0.4554022}& {-0.5489460000}& {-0.1087338888}& {0}\\ {0.2818186}& {-0.5786120000}& {-0.04944333333}& {0.06587839497}\end{array}\right]$ (2)
 > $\mathrm{p1a}≔\mathrm{AddPoint}\left(\mathrm{p1},\left[1.8,0.3920223\right]\right):$
 > $\mathrm{DividedDifferenceTable}\left(\mathrm{p1a}\right)$
 $\left[\begin{array}{ccccc}{0.7651977}& {0}& {0}& {0}& {0}\\ {0.6200860}& {-0.4837056667}& {0}& {0}& {0}\\ {0.4554022}& {-0.5489460000}& {-0.1087338888}& {0}& {0}\\ {0.2818186}& {-0.5786120000}& {-0.04944333333}& {0.06587839497}& {0}\\ {0.3920223}& {-1.102037000}& {-2.617125000}& {-5.135363334}& {-6.501552161}\end{array}\right]$ (3)
 > $\mathrm{xyyp}≔\left[\left[1,1.105170918,0.2210341836\right],\left[1.5,1.252322716,0.3756968148\right],\left[2,1.491824698,0.5967298792\right]\right]$
 ${\mathrm{xyyp}}{≔}\left[\left[{1}{,}{1.105170918}{,}{0.2210341836}\right]{,}\left[{1.5}{,}{1.252322716}{,}{0.3756968148}\right]{,}\left[{2}{,}{1.491824698}{,}{0.5967298792}\right]\right]$ (4)
 > $\mathrm{p2}≔\mathrm{PolynomialInterpolation}\left(\mathrm{xyyp},\mathrm{method}=\mathrm{hermite},\mathrm{function}=\mathrm{exp}\left(0.1{x}^{2}\right),\mathrm{independentvar}='x',\mathrm{errorboundvar}='\mathrm{\xi }',\mathrm{digits}=5\right):$
 > $\mathrm{DividedDifferenceTable}\left(\mathrm{p2}\right)$
 $\left[\begin{array}{cccccc}{1.1052}& {0}& {0}& {0}& {0}& {0}\\ {1.1052}& {0.22103}& {0}& {0}& {0}& {0}\\ {1.2523}& {0.29420}& {0.14634}& {0}& {0}& {0}\\ {1.2523}& {0.37570}& {0.16300}& {0.033320}& {0}& {0}\\ {1.4918}& {0.47900}& {0.20660}& {0.043600}& {0.010280}& {0}\\ {1.4918}& {0.59673}& {0.23546}& {0.057720}& {0.014120}& {0.0038400}\end{array}\right]$ (5)