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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

withStudent[NumericalAnalysis]:

xy:=1.0,0.7651977,1.3,0.6200860,1.6,0.4554022,1.9,0.2818186

xy:=1.0,0.7651977,1.3,0.6200860,1.6,0.4554022,1.9,0.2818186

(1)

p1:=PolynomialInterpolationxy,independentvar='x',method=newton:

DividedDifferenceTablep1

0.76519770000.62008600.4837056667000.45540220.54894600000.108733888800.28181860.57861200000.049443333330.06587839497

(2)

p1a:=AddPointp1,1.8,0.3920223:

DividedDifferenceTablep1a

0.765197700000.62008600.48370566670000.45540220.54894600000.1087338888000.28181860.57861200000.049443333330.0658783949700.39202231.1020370002.6171250005.1353633346.501552161

(3)

xyyp:=1,1.105170918,0.2210341836,1.5,1.252322716,0.3756968148,2,1.491824698,0.5967298792

xyyp:=1,1.105170918,0.2210341836,1.5,1.252322716,0.3756968148,2,1.491824698,0.5967298792

(4)

p2:=PolynomialInterpolationxyyp,method=hermite,function=ⅇ0.1x2,independentvar='x',errorboundvar='ξ',digits=5:

DividedDifferenceTablep2

1.1052000001.10520.2210300001.25230.294200.146340001.25230.375700.163000.033320001.49180.479000.206600.0436000.01028001.49180.596730.235460.0577200.0141200.0038400

(5)

See Also

Student[NumericalAnalysis], Student[NumericalAnalysis][AddPoint], Student[NumericalAnalysis][ApproximateExactUpperBound], Student[NumericalAnalysis][BasisFunctions], Student[NumericalAnalysis][ComputationOverview], Student[NumericalAnalysis][Draw], Student[NumericalAnalysis][InterpolantRemainderTerm], Student[NumericalAnalysis][NevilleTable], Student[NumericalAnalysis][PolynomialInterpolation]


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