LeftPointIntegrator Class

public sealed class LeftPointIntegrator : NumericalIntegrator

Public NotInheritable Class LeftPointIntegrator
	Inherits NumericalIntegrator

public ref class LeftPointIntegrator sealed : public NumericalIntegrator

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

Inheritance

Object  →  ManagedIterativeAlgorithm<Double, Double, SolutionReport<Double, Double>>  →  IterativeAlgorithm<Double>  →  NumericalIntegrator  →  LeftPointIntegrator

The left point rule is one of the simplest numerical integration algorithms around. The interval is divided into smaller intervals, and the function value on the left side 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. It does provide a unique feature in that can produce absolute bounds on the value of the integral of some functions. It produces a lower bound for monotonically increasing integrands, and an upper bound for monotonically decreasing integrands. Complementary bounds are produced by the RightPointIntegrator.

Reference