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Student[NumericalAnalysis]

  

AddPoint

  

return an interpolated polynomial structure with a newly added point

 

Calling Sequence

Parameters

Description

Notes

Examples

Calling Sequence

AddPoint(p, pts)

AddPoint(p, pts, bcs)

Parameters

p

-

a POLYINTERP structure

pts

-

numeric, list(numeric, numeric), list(numeric, numeric,numeric); the new data point (node) to be added

bcs

-

list(numeric, numeric); new boundary conditions for an interpolating polynomial created using the cubic spline method

Description

• 

The AddPoint command takes the point(s) to be added and recomputes the interpolated polynomial from p with the new point(s) and returns the adjusted POLYINTERP structure.

• 

This command is convenient because it prevents you from having to reenter all previous options and data with the new point into the PolynomialInterpolation command or the CubicSpline command to create a new POLYINTERP structure.

• 

If the POLYINTERP structure was created using the CubicSpline command and the boundary conditions are not natural, then new boundary conditions bcs at the end points must be specified.

Notes

• 

This procedure operates numerically; that is, inputs that are not numeric are first evaluated to floating-point numbers before computations proceed.

Examples

withStudent[NumericalAnalysis]:

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

xy:=1.0,0.7651977,1.3,0.6200860,1.6,0.4554022,1.9,0.2818186

(1)

p2PolynomialInterpolationxy,method=neville,extrapolate=1.5:

NevilleTablep2,1.5

0.76519770000.62008600.5233448671000.45540220.51029680020.512471478100.28181860.51326340020.51128566690.5118126939

(2)

Add another node.

p2aAddPointp2,2.2,0.1103623:

The Neville Table now has another row.

NevilleTablep2a,1.5

0.765197700000.62008600.52334486710000.45540220.51029680020.5124714781000.28181860.51326340020.51128566690.511812693900.11036230.51042700020.51373613360.51183021490.5118199942

(3)

See Also

Student[NumericalAnalysis]

Student[NumericalAnalysis][BasisFunctions]

Student[NumericalAnalysis][ComputationOverview]

Student[NumericalAnalysis][CubicSpline]

Student[NumericalAnalysis][DividedDifferenceTable]

Student[NumericalAnalysis][InterpolantRemainderTerm]

Student[NumericalAnalysis][NevilleTable]

Student[NumericalAnalysis][PolynomialInterpolation]

 


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