Home > Extreme Optimization Mathematics Library for .NET > Reference > Extreme.Mathematics.Calculus Namespace
Abstract base class for Gauss-Kronrod type numerical integrators.
For a list of all members of this type, see GaussKronrodIntegrator Members.
System.Object
IterativeAlgorithm
NumericalIntegrator
GaussKronrodIntegrator
GaussKronrodIntegrator is the abstract (MustInherit in Visual Basic) base class for classes that represent Gauss-Kronrod integration rules. Gauss-Kronrod methods use two integration formulas of different orders where the integration points of the lower order formula are also integration points for the higher order formula. This gives a way to estimate the integration error without doing any extra function evaluations.
Classes derived from GaussKronrodIntegrator apply the integration formula to the entire integration interval. They are used most often as integration rules for subintervals in adaptive integration algorithms as implemented by the AdaptiveIntegrator class.
A number of ready-to-use integration rules have been supplied, as listed in the table below.
| Class | Description |
|---|---|
| GaussKronrodIntegrator15 | 7-point Gauss with 15-point Kronrod rule. |
| GaussKronrodIntegrator21 | 10-point Gauss with 21-point Kronrod rule. |
| GaussKronrodIntegrator31 | 15-point Gauss with 31-point Kronrod rule. |
| GaussKronrodIntegrator41 | 20-point Gauss with 41-point Kronrod rule. |
| GaussKronrodIntegrator51 | 25-point Gauss with 51-point Kronrod rule. |
| GaussKronrodIntegrator61 | 30-point Gauss with 61-point Kronrod rule. |
To create a Gauss-Kronrod integrator of a different order, derive your class from GaussKronrodIntegrator, and implement the GetGaussWeights, GetKronrodWeights, and GetKronrodPoints properties. You should also override the Order property to return the order of the integration rule.
Namespace: Extreme.Mathematics.Calculus
Assembly: Extreme.Mathematics (in Extreme.Mathematics.dll)
GaussKronrodIntegrator Members | Extreme.Mathematics.Calculus Namespace