ChebyshevBasis Class

[SerializableAttribute]
public sealed class ChebyshevBasis : FunctionBasis

<SerializableAttribute>
Public NotInheritable Class ChebyshevBasis
	Inherits FunctionBasis

[SerializableAttribute]
public ref class ChebyshevBasis sealed : public FunctionBasis

[<SealedAttribute>]
[<SerializableAttribute>]
type ChebyshevBasis = 
    class
        inherit FunctionBasis
    end

Inheritance

Object  →  FunctionBasis  →  ChebyshevBasis

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(Double, DenseVector<Double>) and FillDerivatives(Double, DenseVector<Double>) 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.

Reference