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Student[NumericalAnalysis]

  

ApproximateValue

  

return specific approximate value(s) of the interpolating polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ApproximateValue(p)

ApproximateValue(p, pts)

Parameters

p

-

a POLYINTERP structure

pts

-

(optional) numeric, list(numeric); a point or list of points at which the value of the approximating polynomial is to be computed

Description

• 

The ApproximateValue command computes the value(s) of the approximated polynomial at specified point(s) pts or at the extrapolated point(s) from the POLYINTERP structure, depending on whether pts is specified or not.

• 

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

• 

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

Examples

withStudent[NumericalAnalysis]:

xy1.0,0.7651977,1.3,0.6200860,1.6,0.4554022,1.9,0.2818186

xy1.0,0.7651977,1.3,0.6200860,1.6,0.4554022,1.9,0.2818186

(1)

p1PolynomialInterpolationxy,method=neville,extrapolate=1.5:

ApproximateValuep1

1.5,0.5118126939

(2)

ApproximateValuep1,1.7,1.8

1.7,0.3980028398,1.8,0.3400098828

(3)

xyy0,1,12,1,1,1110,32,34,2,78,52,910,3,1110,72,1

xyy0,1,12,1,1,1110,32,34,2,78,52,910,3,1110,72,1

(4)

p2CubicSplinexyy,independentvar='x':

ApproximateValuep2,1.3

1.3,0.8776545517

(5)

See Also

Student[NumericalAnalysis]

Student[NumericalAnalysis][AddPoint]

Student[NumericalAnalysis][ApproximateExactUpperBound]

Student[NumericalAnalysis][BasisFunctions]

Student[NumericalAnalysis][ComputationOverview]

Student[NumericalAnalysis][CubicSpline]

Student[NumericalAnalysis][Draw]

Student[NumericalAnalysis][InterpolantRemainderTerm]

Student[NumericalAnalysis][PolynomialInterpolation]

 


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