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Student[NumericalAnalysis]

  

ExactValue

  

return specific value(s) of the exact function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ExactValue(p)

ExactValue(p, pts)

Parameters

p

-

a POLYINTERP structure

pts

-

(optional) numeric, list(numeric); a point or list of points at which the value of the exact function is computed

Description

• 

The ExactValue command computes the value(s) of the exact function at specified point(s) pts or at the extrapolated point(s) from the POLYINTERP structure, depending on whether pts is given or not.

• 

The exact values are returned in a list of the form [[point[i], exacti], [...], ...], i = 1..number of points.

• 

If the ExactValue command is used on a POLYINTERP structure whose exact function was not originally specified, an exception will be raised.

• 

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

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':

ExactValuep1

0.25,2.378414230,0.75,1.681792830,1.25,1.189207114

(2)

ExactValuep1,0.5,1.0

0.5,5.80119965710-10,1.0,2.

(3)

See Also

Student[NumericalAnalysis]

Student[NumericalAnalysis][ApproximateExactUpperBound]

Student[NumericalAnalysis][ApproximateValue]

Student[NumericalAnalysis][ComputationOverview]

Student[NumericalAnalysis][CubicSpline]

Student[NumericalAnalysis][DataPoints]

Student[NumericalAnalysis][InterpolantRemainderTerm]

Student[NumericalAnalysis][PolynomialInterpolation]

Student[NumericalAnalysis][RemainderTerm]

 


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