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Student[NumericalAnalysis]

  

ApproximateExactUpperBound

  

compute approximate, exact and upper bound remainder term values

 

Calling Sequence

Parameters

Description

Notes

Examples

Calling Sequence

ApproximateExactUpperBound(p)

ApproximateExactUpperBound(p, pts)

Parameters

p

-

a POLYINTERP structure

pts

-

(optional) algebraic, list(algebraic); the point(s) at which the approximating polynomial, the exact value(s) of the function, and the upper bound(s) of the remainder term are computed

Description

• 

The ApproximateExactUpperBound command computes three values: the approximating polynomial, the exact value of the function and the upper bound of the remainder term, for each point specified in pts.

• 

If pts is not specified, the extrapolated points in the given POLYINTERP structure are used instead.

• 

The computed values are returned in the form of a list: [pts, approximate values, exact values, upper bounds].

• 

The POLYINTERP structure is created using the PolynomialInterpolation command.

Notes

• 

POLYINTERP structures whose interpolation method is the cubic spline method may not be used with this 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:

ApproximateExactUpperBoundp1

0.25,2.685058594,2.378414230,1.793805002,0.75,1.746582031,1.681792830,0.4892195461,1.25,1.166503906,1.189207114,0.2717886368

(2)

ApproximateExactUpperBoundp1,0.5,1.5

0.5,0.,5.80119965710-10,0.,1.5,0.,8.70179948210-10,0.

(3)

See Also

Student[NumericalAnalysis]

Student[NumericalAnalysis][ComputationOverview]

Student[NumericalAnalysis][ExactValue]

Student[NumericalAnalysis][InterpolantRemainderTerm]

Student[NumericalAnalysis][PolynomialInterpolation]

Student[NumericalAnalysis][RemainderTerm]

 


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