﻿GaussKronrod21Integrator Class

# GaussKronrod21Integrator Class

Class GaussKronrod21Integrator calculates an approximation of the integral of a function over a finite interval using the Gauss 10-point and the Kronrod 21-point rule.
Inheritance Hierarchy

Namespace:  CenterSpace.NMath.Core
Assembly:  NMath (in NMath.dll) Version: 7.3
Syntax
```[SerializableAttribute]
public class GaussKronrod21Integrator : IIntegrator,
ICloneable```

The GaussKronrod21Integrator type exposes the following members.

Constructors
NameDescription
GaussKronrod21Integrator
Default constructor. Constructs a GaussKronrodIntegrator instance that can be used to integrate a function.
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Properties
NameDescription
PreviousEstimate
Gets the integral approximation calculated using the Gauss 10-point rule.
RelativeErrorEstimate
Gets an estimate of the relative error for the integral approximation.
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Methods
NameDescription
Clone
Creates a deep copy of this integrator.
GetGauss10PointEstimate
Gets the 10 point Gauss Quadrature estimate of the integral of the function.
InitialEstimate
Calculates the Kronrod 21 point integral approximation and initializes instance data.
Integrate(OneVariableFunction, DoubleVector, DoubleVector)
Uses the Gauss Kronrod algorithm to integrate the specified function using the specified nodes and weights.
Integrate(OneVariableFunction, Double, Double)
Estimates the integral of the specified function over the specified interval.
RescaleError
Rescales the absolute error estimate to a relative one.
Translate
Function that maps translates points to the integral of integration.
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Fields
NameDescription
absFunctionEstimate_
Value if the integral of the absolute value of the integrand.
absScaledFunctionEstimate_
Value of the integral of the absolute value of the integrand minus the estimate of the integrands integral.
functionValueAtCenter_
Value of the integrand at the center of the interval.
functionValues_
Saved function values.
intervalCenter_
The center of the integration interval.
intervalHalfLength_
Half length of the integration interval.
nodesG10_
Nodes for Gauss 10 point quadrature.
nodesGK21_
Nodes for Gauss Kronrod 21 point quadrature.
previousEstimate_
The integral approximation calculated using the Gauss 10-point rule.
previousEstimateName
relativeErrorEstimate_
Estimate of the relative error.
relativeErrorEstimateName
weightsG10_
Weights for Gauss 10 point quadrature.
weightsGK21_
Weights for Gauss Kronrod 21 point quadrature.
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Remarks
The Gauss-Konrod algorithm is especially suited for non-singular oscillating integrands.