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Student[NumericalAnalysis]

  

BasisFunctions

  

return a list of the basis functions from a POLYINTERP structure

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

BasisFunctions(p)

BasisFunctions(p, indvar)

Parameters

p

-

a POLYINTERP structure

invar

-

(optional) name; the name to assign to the independent variable in the basis functions that are returned

Description

• 

The BasisFunctions routine retrieves the basis functions from a POLYINTERP structure.

• 

The POLYINTERP structure is created using the PolynomialInterpolation command.

• 

Only POLYINTERP structures that contain data points that have been interpolated using the Lagrange, Newton or Hermite methods can use the BasisFunctions 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:

BasisFunctionsp1

0.08888888889x0.5x1.0x1.5x2.0x2.5x3.0,0.5333333333xx1.0x1.5x2.0x2.5x3.0,1.333333333xx0.5x1.5x2.0x2.5x3.0,1.777777778xx0.5x1.0x2.0x2.5x3.0,1.333333333xx0.5x1.0x1.5x2.5x3.0,0.5333333333xx0.5x1.0x1.5x2.0x3.0,0.08888888889xx0.5x1.0x1.5x2.0x2.5

(2)

Drawp1,objects=BasisFunctions

xyyp1,1.105170918,0.2210341836,1.5,1.252322716,0.3756968148,2,1.491824698,0.5967298792

xyyp:=1,1.105170918,0.2210341836,1.5,1.252322716,0.3756968148,2,1.491824698,0.5967298792

(3)

p2PolynomialInterpolationxyyp,method=hermite,function=ⅇ0.1x2,independentvar='x',errorboundvar='ξ',digits=5:

BasisFunctionsp2

1,x1.,x1.2,x1.2x1.5,x1.2x1.52,x1.2x1.52x2.

(4)

See Also

Student[NumericalAnalysis]

Student[NumericalAnalysis][AddPoint]

Student[NumericalAnalysis][ComputationOverview]

Student[NumericalAnalysis][Draw]

Student[NumericalAnalysis][PolynomialInterpolation]

Student[NumericalAnalysis][RemainderTerm]

 


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