PolynomialBasis Class

[SerializableAttribute]
public class PolynomialBasis : FunctionBasis

<SerializableAttribute>
Public Class PolynomialBasis
	Inherits FunctionBasis

[SerializableAttribute]
public ref class PolynomialBasis : public FunctionBasis

[<SerializableAttribute>]
type PolynomialBasis =  
    class
        inherit FunctionBasis
    end

The PolynomialBasis type exposes the following members.

	Name	Description
	PolynomialBasis	Constructs a new GeneralFunctionBasis from an array of function of one variable delegates.

	Name	Description
	Item	Gets an element of the collection as a function of one variable. (Overrides FunctionBasisItemInt32.)
	Length	Gets the number of items in this FunctionBasis. (Inherited from FunctionBasis.)

	Name	Description
	DerivativesAt	Evaluates the derivatives of the member functions of this FunctionBasis at a specified value. (Inherited from FunctionBasis.)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	FillDerivatives(Double, DenseVectorDouble)	Fills a vector with the derivatives of the member functions at a specified value. (Overrides FunctionBasisFillDerivatives(Double, DenseVectorDouble).)
	FillDerivatives(VectorDouble, DenseMatrixDouble)	Fills the rows of a DenseMatrixT with the values of the member functions of a FunctionBasis evaluated for each element in a Vector. (Inherited from FunctionBasis.)
	FillValues(Double, DenseVectorDouble)	Fills a dense vector with the values of the member functions at a specified value. (Overrides FunctionBasisFillValues(Double, DenseVectorDouble).)
	FillValues(VectorDouble, DenseMatrixDouble)	Fills the rows of a DenseMatrixT with the values of the member functions of a FunctionBasis evaluated for each element in a Vector. (Inherited from FunctionBasis.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetFunction(Double)	Obsolete. Constructs a new LinearCombination from the functions in this instance. (Inherited from FunctionBasis.)
	GetFunction(VectorDouble)	Constructs a new Polynomial with the specified coefficients. (Overrides FunctionBasisGetFunction(VectorDouble).)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	LeastSquaresFit(VectorDouble, VectorDouble)	Gets the least squares fit of target data in terms of the components of the FunctionBasis. (Inherited from FunctionBasis.)
	LeastSquaresFit(Double, Double, Double)	Gets the least squares fit of target data in terms of the components of the FunctionBasis. (Inherited from FunctionBasis.)
	LeastSquaresFit(Double, Double, Int32)	Gets the least squares fit of target data in terms of the components of the FunctionBasis. (Inherited from FunctionBasis.)
	LeastSquaresFit(VectorDouble, VectorDouble, VectorDouble)	Gets the least squares fit of target data in terms of the components of the FunctionBasis. (Inherited from FunctionBasis.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)
	ValuesAt	Evaluates the member functions of this FunctionBasis at a specified value. (Inherited from FunctionBasis.)

Use a PolynomialBasis object to represent a basis for the polynomials. Only in rare cases will it be necessary to construct a PolynomialBasis, as most functionality is available through the Polynomial class.

The basis functions of a PolynomialBasis are the monomials of degree 0 up to and including the specified degree.

The Chebyshev polynomials form an alternate basis for the polynomials and have many desirable numerical properties.

Reference