BarycentricBasis Class

public class BarycentricBasis : FunctionBasis

Public Class BarycentricBasis
	Inherits FunctionBasis

public ref class BarycentricBasis : public FunctionBasis

type BarycentricBasis =  
    class
        inherit FunctionBasis
    end

The BarycentricBasis type exposes the following members.

	Name	Description
	BarycentricBasis	Constructs a new barycentric basis with the specified set of support points and corresponding weights.

	Name	Description
	Item	Gets an element of the collection as a function of one variable. (Inherited from FunctionBasis.)
	Length	Gets the number of items in this FunctionBasis. (Inherited from FunctionBasis.)
	SupportPoints	Gets the support points of the basis.
	Weights	Gets the weights of the basis.

	Name	Description
	Chebyshev(Int32)	Returns a new BarycentricBasis equivalent to a basis of Chebyshev polynomials of the specified degree over the interval [-1, 1].
	Chebyshev(Double, Double, Int32)	Returns a new BarycentricBasis equivalent to a basis of Chebyshev polynomials of the specified degree over the specified interval.
	Chebyshev2(Int32)	Returns a new BarycentricBasis equivalent to a basis of Chebyshev polynomials of the second kind of the specified degree over the interval [-1, 1].
	Chebyshev2(Double, Double, Int32)	Returns a new BarycentricBasis equivalent to a basis of Chebyshev polynomials of the second kind of the specified degree over the specified interval.
	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 of a FunctionBasis 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.)
	FloaterHormann(VectorDouble, Int32)	Constructs a new barycentric basis for Floater-Hormann rational interpolation of the specified order through the specified support points.
	FloaterHormann(Double, Double, Int32, Int32)	Constructs a new barycentric basis for Floater-Hormann rational interpolation through a set of equidistant support points.
	GetFunction(Double)	Obsolete. Constructs a new LinearCombination from the functions in this instance. (Inherited from FunctionBasis.)
	GetFunction(VectorDouble)	Constructs a new LinearCombination from the functions in this instance. (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.)
	Polynomial(VectorDouble)	Constructs a new barycentric basis equivalent to Lagrange polynomial interpolation through the specified support points.
	Polynomial(Double, Double, Int32)	Returns a new BarycentricBasis equivalent to a basis of Lagrange polynomials over an equidistant set of points.
	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 the BarycentricBasis class to represent the basis of a set of rational functions in barycentric form. All functions in the set have the same support points or nodes and corresponding weights.

The rational functions that can be represented in the basis are linear combinations of the basis functions.

For a specific set of support points, there is one set of weights for which all basis functions are polynomials. A barycentric basis is therefore a generalization of a polynomial basis.

Reference