MidpointIntegrator<T> Class

public sealed class MidpointIntegrator<T> : NumericalIntegrator<T>
where T : Object, INumber<T>

Public NotInheritable Class MidpointIntegrator(Of T As {Object, INumber(Of T)})
	Inherits NumericalIntegrator(Of T)

generic<typename T>
where T : Object, INumber<T>
public ref class MidpointIntegrator sealed : public NumericalIntegrator<T>

[<SealedAttribute>]
type MidpointIntegrator<'T when 'T : Object and INumber<'T>> = 
    class
        inherit NumericalIntegrator<'T>
    end

Inheritance

Object  →  ManagedIterativeAlgorithm<T, T, SolutionReport<T, T>>  →  IterativeAlgorithm<T>  →  NumericalIntegrator<T>  →  MidpointIntegrator<T>

Type Parameters

T

The right point rule is one of the simplest numerical integration algorithms around. The interval is divided into smaller intervals, and the function value in the middle of the subinterval is taken as an approximation for the function over the entire subinterval.

This algorithm is of order 1. In each iteration, the number of points is doubled. The difference between successive approximations is taken as the estimate for the integration error.

Because the order of the algorithm is so low, use of this algorithm is not generally recommended for general use. The fact that previous integration points are not re-used makes this algorithm extra inefficient. However, it does provide a unique feature in that can produce absolute bounds on the value of the integral of some functions. It produces an upper bound for concave integrands, and a lower bound for convex integrands. Complementary bounds are produced by the TrapezoidIntegrator<T>.

Reference