perform polynomial interpolation on a set of data - Maple Help

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Student[NumericalAnalysis][PolynomialInterpolation] - perform polynomial interpolation on a set of data

Calling Sequence

PolynomialInterpolation(xy, opts)

Parameters

xy

-

list(numeric), list(list(numeric, numeric)), list(list(numeric, numeric, numeric)); the data points to be interpolated

opts

-

equation(s) of the form keyword=value where keyword is one of digits, errorboundvar, extrapolate, function, independentvar, method; the options for interpolating the data xy

Description

• 

The PolynomialInterpolation command interpolates the given data points xy and stores all computed information in a POLYINTERP structure.

• 

The POLYINTERP structure is then passed around to different interpolation commands in the Student[NumericalAnalysis] subpackage where information can be extracted from it and, depending on the command, manipulated.

Notes

• 

When the Hermite method is used to perform interpolation, xy must be of the form list(list(numeric, numeric, numeric)).

• 

This procedure operates numerically; that is, inputs that are not numeric are first evaluated to floating-point numbers before computations proceed.

Examples

withStudent[NumericalAnalysis]:

xy:=0,1,12,1,1,1110,32,34,2,78,52,910,3,1110,72,1

xy:=0,1,12,1,1,1110,32,34,2,78,52,910,3,1110,72,1

(1)

L:=PolynomialInterpolationxy,independentvar=x,method=lagrange:

Nev:=PolynomialInterpolationxy,independentvar=x,method=neville:

New:=PolynomialInterpolationxy,independentvar=x,method=newton:

expandInterpolantL

1+225475x2+73320x43296225x5+22175x653225x71722473600x381831200x

(2)

expandInterpolantNev

1+225475x2+73320x43296225x5+22175x653225x71722473600x381831200x

(3)

expandInterpolantNew

1+225475x2+73320x43296225x5+22175x653225x71722473600x381831200x

(4)

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

(5)

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

RemainderTermp2

17200.120ⅇ0.1ξ2+0.0720ξ2ⅇ0.1ξ2+0.00480ξ4ⅇ0.1ξ2+0.000064ξ6ⅇ0.1ξ2x1.2x1.52x2.2 &where 1.ξandξ2.

(6)

DividedDifferenceTablep2

1.1052000001.10520.2210300001.25230.294200.146340001.25230.375700.163000.033320001.49180.479000.206600.0436000.01028001.49180.596730.235460.0577200.0141200.0038400

(7)

Drawp2

See Also

Student[NumericalAnalysis], Student[NumericalAnalysis][AddPoint], Student[NumericalAnalysis][BasisFunctions], Student[NumericalAnalysis][ComputationOverview], Student[NumericalAnalysis][CubicSpline], Student[NumericalAnalysis][DataPoints], Student[NumericalAnalysis][ExactValue], Student[NumericalAnalysis][InterpolantRemainderTerm]


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