LeftPointIntegrator Class

Members See Also

Represents a numerical integrator that uses the left point rule.

Namespace: Extreme.Mathematics.Calculus
Assembly: Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 4.2.11333.0 (4.2.12253.0)

Syntax

C#
public sealed class LeftPointIntegrator : NumericalIntegrator

Visual Basic (Declaration)
Public NotInheritable Class LeftPointIntegrator _ Inherits NumericalIntegrator

Visual C++
public ref class LeftPointIntegrator sealed : public NumericalIntegrator

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

Remarks

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.

Inheritance Hierarchy

System..::..Object
  Extreme.Mathematics.Algorithms..::..ManagedIterativeAlgorithm<(Of <(<'Double>)>)>
    Extreme.Mathematics.Algorithms..::..IterativeAlgorithm
      Extreme.Mathematics.Calculus..::..NumericalIntegrator
        Extreme.Mathematics.Calculus..::..LeftPointIntegrator