RombergIntegrator Class

public sealed class RombergIntegrator : NumericalIntegrator

Public NotInheritable Class RombergIntegrator
	Inherits NumericalIntegrator

public ref class RombergIntegrator sealed : public NumericalIntegrator

[<SealedAttribute>]
type RombergIntegrator =  
    class
        inherit NumericalIntegrator
    end

The RombergIntegrator type exposes the following members.

	Name	Description
	RombergIntegrator	Constructs a new RombergIntegrator object.

	Name	Description
	AbsoluteTolerance	Gets or sets the absolute tolerance used in the convergence test. (Inherited from IterativeAlgorithm.)
	ConvergenceCriterion	Gets or sets a value specifying the criterion that is to be used in the convergence test for the algorithm. (Inherited from IterativeAlgorithm.)
	ConvergenceTest	Gets the convergence test for the algorithm. (Inherited from IterativeAlgorithm.)
	ConvergenceTests	Gets the collection of convergence tests for the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	EstimatedError	Gets a value indicating the size of the absolute error of the result. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	EvaluationsNeeded	Gets the number of evaluations needed to execute the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	HasSharedDegreeOfParallelism	Indicates whether the degree of parallelism is a property that is shared across instances. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	Integrand	Gets or sets the function to integrate. (Inherited from NumericalIntegrator.)
	IterationsNeeded	Gets the number of iterations needed by the algorithm to reach the desired accuracy. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	LowerBound	Gets or sets the lower bound of the integration interval. (Inherited from NumericalIntegrator.)
	MaxDegreeOfParallelism	Gets or sets the maximum degree of parallelism enabled by this instance. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	MaxEvaluations	Gets or sets the maximum number of evaluations during the calculation. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	MaxIterations	Gets or sets the maximum number of iterations to use when approximating the roots of the target function. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	MinIterations	Gets or sets the minimum iterations that have to be performed. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	Order	Gets the order of the numerical integrator. (Overrides NumericalIntegratorOrder.)
	ParallelOptions	Gets or sets the configuration for the parallel behavior of the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	RelativeTolerance	Gets or sets the relative tolerance used in the convergence test. (Inherited from IterativeAlgorithm.)
	Result	Gets the result of an algorithm after it has executed. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	SolutionReport	Gets the result of an algorithm after it has executed. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	Status	Gets the AlgorithmStatus following an execution of the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	ThrowExceptionOnFailure	Gets or sets a value indicating whether to throw an exception when the algorithm fails to converge. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	UpperBound	Gets or sets the upper bound of the integration interval. (Inherited from NumericalIntegrator.)

	Name	Description
	Clone	Returns a copy of this numerical integrator object. (Overrides NumericalIntegratorClone.)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Integrate	Numerically integrates a function of one variable. (Inherited from NumericalIntegrator.)
	Integrate(ParallelOptions)	Numerically integrates a function of one variable. (Inherited from NumericalIntegrator.)
	Integrate(Double, Double)	Numerically integrates a function of one variable. (Inherited from NumericalIntegrator.)
	Integrate(Double, Double, ParallelOptions)	Numerically integrates a function of one variable. (Inherited from NumericalIntegrator.)
	Integrate(FuncDouble, Double, Double, Double)	Numerically integrates a function of one variable. (Inherited from NumericalIntegrator.)
	Integrate(FuncDouble, Double, Double, Double, ParallelOptions)	Numerically integrates a function of one variable. (Inherited from NumericalIntegrator.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

Romberg integration is an enhancement of the basic trapezoid rule. The number of points is doubled in each iteration. The successive approximations are then used to extrapolate the exact value of the integral as the width of each subinterval approaches zero. Romberg integration has an effective order of 2k after k steps of the algorithm. Even though the number of function evaluations is still fairly high, it is a major improvement over Simpson's rule, and a reasonable choice for integrands that are sufficiently smooth.

Reference