Assembly: Extreme.Numerics (Extreme.Numerics)
Syntax
| Visual Basic (Declaration) |
|---|
Public NotInheritable Class ChebyshevSeries _ Inherits PolynomialBase |
| C# |
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public sealed class ChebyshevSeries : PolynomialBase |
| C++ |
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public ref class ChebyshevSeries sealed : public PolynomialBase |
Methods
| Icon | Type | Description |
|---|---|---|
 | Add(Double, LinearCombination) |
Adds two Chebyshev series.
|
| Add(LinearCombination) |
Adds another LinearCombination to this instance.
|
| Clone() |
Constructs an exact copy of this instance.
|
| Equals(Object) | |
 | Finalize() | |
| FindRoots() |
Gets the set of X-coordinates where the curve crosses
the X-axis.
|
| GetCurveFitter() |
Returns a CurveFitter object that can be used to fit the curve to data.
|
| GetDerivative() |
Returns a Curve that represents the derivative
of this ChebyshevSeries.
|
| GetHashCode() | Serves as a hash function for a particular type. |
 | GetInterpolatingPolynomial(RealFunction, Double, Double, Int32) |
Calculates the Chebyshev interpolating polynomial of the specified degree
over the given interval for the specified function.
|
| GetType() | Gets the Type of the current instance. |
| Integral(Double, Double) |
Gets the definite integral of the ChebyshevSeries
between the specified X-coordinates.
|
| LeastSquaresFit(Double[](), Double[](), Double, Double, Int32) |
Returns the Polynomial that is the best
least squares fit through the given set of points.
|
| LeastSquaresFit(Double[](), Double[](), Int32) |
Returns the Polynomial that is the best
least squares fit through the given set of points.
|
| MemberwiseClone() | Creates a shallow copy of the current Object. |
| OnParameterChanged(Int32, Double) |
Called when a coefficient of the polynomial is changed.
|
| OnParameterChanging(Int32, Double) |
Called before the value of a curve parameter is changed.
|
| Reduce() |
Reduces the degree of a polynomial so that the leading coefficient is different
from zero.
|
| Reduce(Double) |
Reduces the degree of a polynomial so that the leading coefficient is greater than
the specified tolerance.
|
| SlopeAt(Double) |
Evaluates the slope or first derivative of a Chebyshev
series for a DoubleComplex argument.
|
| Subtract(LinearCombination) |
Subtracts another LinearCombination from this instance.
|
| TangentAt(Double) |
Gets the tangent Line to the curve at the
specified X-coordinate.
|
| ToString() | |
| ValueAt(Double) |
Evaluates the Chebyshev series for a real argument.
|
Constructors
| Icon | Type | Description |
|---|---|---|
| ChebyshevSeriesNew(Int32) |
Constructs a new ChebyshevSeries of the specified
degree over the interval [-1, 1].
|
| ChebyshevSeriesNew(Double, Double, Int32) |
Constructs a new ChebyshevSeries of the specified
degree over the specified interval.
|
| ChebyshevSeriesNew(Double[]()) |
Constructs a new ChebyshevSeries with the
specified coefficients over the interval [-1, 1].
|
| ChebyshevSeriesNew(Double, Double, Double[]()) |
Constructs a new ChebyshevSeries with the
specified coefficients over the specified interval.
|
Properties
| Icon | Type | Description |
|---|---|---|
 | Basis |
Gets the function basis for the polynomial.
|
| Coefficient(Int32) |
Gets or sets the coefficient of the function with the specified
index.
|
| Degree |
Gets the degree of the polynomial.
|
| Item(Int32) |
Gets or sets the coefficient of the function with the specified
index.
|
| LowerBound |
Gets or sets the lower bound of the interval over which this ChebyshevSeries is defined.
|
| Parameters |
Gets the collection of parameters that determine the shape of this
Curve.
|
| UpperBound |
Gets or sets the upper bound of the interval over which this ChebyshevSeries is defined.
|
Remarks
The Chebyshev polynomials provide an alternate basis for representating general polynomials. Two characteristics make Chebyshev polynomials especially attractive. They are mutually orthogonal, and there exists a simple recurrence relation between consecutive polynomials.
Chebyshev polynomials are defined over the interval [-1, 1]. Using Chebyshev expansions outside of this interval is usually not meaningful and is to be avoided. To allow expansions over any finite interval, transformations are applied wherever necessary.
The ChebyshevSeries class inherits from PolynomialBase This class defines a number of properties shared by all polynomial classes. PolynomialBase is itself derived from LinearCombination.
The Parameters of a Chebyshev series are the coefficients of the polynomial.
The Degree of a Chebyshev series is the highest degree of a Chebyshev polynomial that appears in the sum. The number of parameters of the series equals the degree plus one.
Inheritance Hierarchy
Extreme.Mathematics.Curves.Curve
Extreme.Mathematics.Curves.LinearCombination
Extreme.Mathematics.Curves.PolynomialBase
Extreme.Mathematics.Curves.ChebyshevSeries
