Represents a
FunctionBasis for the polynomials
up to a specified degree.
SystemObject Extreme.Mathematics.CurvesFunctionBasis Extreme.Mathematics.CurvesPolynomialBasis
Namespace:
Extreme.Mathematics.Curves
Assembly:
Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.1
[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.
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| 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) | (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) | (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. (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.) |
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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