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Student[NumericalAnalysis]

  

RemainderTerm

  

return the remainder term from an interpolation structure

 

Calling Sequence

Parameters

Options

Description

Notes

Examples

Calling Sequence

RemainderTerm(p, opts)

Parameters

p

-

a POLYINTERP structure

opts

-

(optional) equation(s) of the form keyword=value, where keyword is: errorboundvar; options for returning the remainder term

Options

• 

errorboundvar = name

  

The name to assign to the independent variable in the remainder term.

Description

• 

The RemainderTerm command returns the remainder term from the POLYINTERP structure p.

• 

The POLYINTERP structure is created using the PolynomialInterpolation command.

• 

In order for the remainder term to exist, the POLYINTERP structure p must have an associated exact function, given through the PolynomialInterpolation command.

Notes

• 

POLYINTERP structures that were created with the CubicSpline command cannot be used with the RemainderTerm command, since they do not have a remainder term.

• 

A remainder term is also called an error term.

Examples

withStudent[NumericalAnalysis]:

xy0,4.0,0.5,0,1.0,2.0,1.5,0,2.0,1.0,2.5,0,3.0,0.5

xy:=0,4.0,0.5,0,1.0,2.0,1.5,0,2.0,1.0,2.5,0,3.0,0.5

(1)

p1PolynomialInterpolationxy,function=22xcosπx,method=lagrange,extrapolate=0.25,0.75,1.25,errorboundvar='ξ':

RemainderTermp1

1504022ξln27cosπξ722ξln26πsinπξ+2122ξln25π2cosπξ+3522ξln24π3sinπξ3522ξln23π4cosπξ2122ξln22π5sinπξ+722ξln2π6cosπξ+22ξπ7sinπξxx0.5x1.0x1.5x2.0x2.5x3.0 &where 0.ξandξ3.0

(2)

xyyp1,1.105170918,0.2210341836,1.5,1.252322716,0.3756968148,2,1.491824698,0.5967298792

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

(3)

p2PolynomialInterpolationxyyp,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.

(4)

See Also

Student[NumericalAnalysis]

Student[NumericalAnalysis][ApproximateExactUpperBound]

Student[NumericalAnalysis][ApproximateValue]

Student[NumericalAnalysis][ComputationOverview]

Student[NumericalAnalysis][DataPoints]

Student[NumericalAnalysis][ExactValue]

Student[NumericalAnalysis][InterpolantRemainderTerm]

Student[NumericalAnalysis][PolynomialInterpolation]

 


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