﻿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
SystemObject
CenterSpace.NMath.CoreGaussKronrod21Integrator
CenterSpace.NMath.CoreGaussKronrod43Integrator

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4
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.