return the interpolating polynomial and remainder term from an interpolation structure - Maple Help

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Student[NumericalAnalysis][InterpolantRemainderTerm] - return the interpolating polynomial and remainder term from an interpolation structure

Calling Sequence

InterpolantRemainderTerm(p, opts)




a POLYINTERP structure



(optional) equations of the form keyword=value where keyword is one of errorboundvar, independentvar, showapproximatepoly, showremainder; options for returning the interpolant and remainder term



The InterpolantRemainderTerm command returns the approximate polynomial and remainder term from a POLYINTERP structure.


The interpolant and remainder term are returned in an expression sequence of the form Pn, Rn, where Pn is the interpolant and Rn is the remainder term.


The POLYINTERP structure is created using the PolynomialInterpolation command or the CubicSpline command.


If the POLYINTERP structure p was created using the CubicSpline command then the InterpolantRemainderTerm command can only return the approximate polynomial and therefore showremainder must be set to false.


In order for the remainder term to exist, the POLYINTERP structure p must have an associated exact function that has been given.



The remainder term is also called an error term.


The interpolant is also called the approximating polynomial or interpolating polynomial.








0.3555555556x0.5x1.0x1.5x2.0x2.5x3.02.666666667xx0.5x1.5x2.0x2.5x3.0+1.333333333xx0.5x1.0x1.5x2.5x3.00.04444444444xx0.5x1.0x1.5x2.0x2.5,1504022ξln27cosπξ722ξln26πsinπξ+2122ξln25π2cosπξ+3522ξln24π3sinπξ3522ξln23π4cosπξ2122ξln22π5sinπξ+722ξln2π6cosπξ+22ξπ7sinπξxx0.5x1.0x1.5x2.0x2.5x3.0 &where 0.ξandξ3.0


See Also

Student[NumericalAnalysis], Student[NumericalAnalysis][ComputationOverview], Student[NumericalAnalysis][CubicSpline], Student[NumericalAnalysis][Interpolant], Student[NumericalAnalysis][PolynomialInterpolation], Student[NumericalAnalysis][RemainderTerm], Student[NumericalAnalysis][UpperBoundOfRemainderTerm]

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