Student[NumericalAnalysis] - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Education : Student Packages : Numerical Analysis : Computation : Student/NumericalAnalysis/UpperBoundOfRemainderTerm

Student[NumericalAnalysis]

  

UpperBoundOfRemainderTerm

  

compute the upper bound of the remainder term at a given point

 

Calling Sequence

Parameters

Description

Notes

Examples

Calling Sequence

UpperBoundOfRemainderTerm(p)

UpperBoundOfRemainderTerm(p, pts)

Parameters

p

-

a POLYINTERP structure

pts

-

(optional) numeric, list(numeric); a point or list of points at which the upper bound(s) of the remainder term are computed

Description

• 

The UpperBoundOfRemainderTerm command returns the value(s) of upper bound of the remainder term of the approximated polynomial at the specified point(s) pts or at the extrapolated point(s) from the POLYINTERP structure, depending on whether pts is specified or not.

• 

The pts must be within the range of the approximating polynomial.

• 

The upper bounds are returned in a list of the form: [[pointi, upperboundi, [...], ...], i=1..number of points.

• 

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

• 

In order for the upper bound to be computed, the POLYINTERP structure p must have an associated function, given by the PolynomialInterpolation command.

• 

If the POLYINTERP structure was created with the CubicSpline command, the boundary conditions must be clamped.

Notes

• 

A remainder term is sometimes called an error term.

Examples

withStudentNumericalAnalysis:

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

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

(1)

p1PolynomialInterpolationxy,function=22xcosPix,method=lagrange,extrapolate=1.25,errorboundvar='ξ':

UpperBoundOfRemainderTermp1

1.25,0.2717886368

(2)

UpperBoundOfRemainderTermp1,1.7

1.7,0.2519320807

(3)

See Also

Student[NumericalAnalysis]

Student[NumericalAnalysis][ApproximateExactUpperBound]

Student[NumericalAnalysis][ApproximateValue]

Student[NumericalAnalysis][ComputationOverview]

Student[NumericalAnalysis][ExactValue]

Student[NumericalAnalysis][PolynomialInterpolation]

Student[NumericalAnalysis][RemainderTerm]