ChebyshevBasis Class

Represents a FunctionBasis made up of Chebyshev polynomials over a specified interval up to a specified degree.

For a list of all members of this type, see ChebyshevBasis Members.

System.Object
   FunctionBasis
      ChebyshevBasis

Remarks

Use a ChebyshevBasis object to represent a basis for the polynomials in terms of Chebyshev polynomials over a specified interval. A number of mathematical properties of Chebyshev polynomials - in particular their mutual orthogonality over the interval [-1, 1] - make this basis particularly useful for numerical applications.

Chebyshev polynomials have these special properties only over the interval [-1,1]. However, rescaling is applied transparently to allow a ChebyshevBasis to be defined over any finite interval.

Only in rare cases will it be necessary to construct a ChebyshevBasis, as most functionality is available through the ChebyshevSeries class. The most useful members are the FillValues and FillDerivatives methods, which allow for efficient calculation of multiple values or derivatives of the polynomials.

Note: The first function (the constant term) is equal to 0.5 instead of the value of 1 of the Chebyshev polynomial of degree 0. The reason is that Chebyshev series are commonly expressed with the constant term multiplied by 0.5. The ChebyshevSeries class follows this convention.

Requirements

Namespace: Extreme.Mathematics.Curves

Assembly: Extreme.Mathematics (in Extreme.Mathematics.dll)

See Also

ChebyshevBasis Members | Extreme.Mathematics.Curves Namespace | FunctionBasis | ChebyshevSeries | PolynomialBasis