Extreme Optimization™: Complexity made simple.

Math and Statistics
Libraries for .NET
  • Home
  • Features
    • Math Library
    • Vector and Matrix Library
    • Statistics Library
    • Performance
    • Usability
  • Documentation
    • Introduction
    • Math Library User's Guide
    • Vector and Matrix Library User's Guide
    • Statistics Library User's Guide
    • Reference
  • Resources
    • Downloads
    • QuickStart Samples
    • Sample Applications
    • Frequently Asked Questions
    • Technical Support
  • Blog
  • Order
  • Company
    • About us
    • Testimonials
    • Customers
    • Press Releases
    • Careers
    • Contact us
Introduction
Deployment Guide
Using Parallelism
Expand Mathematics Library User's GuideMathematics Library User's Guide
Expand Vector and Matrix Library User's GuideVector and Matrix Library User's Guide
Expand Statistics Library User's GuideStatistics Library User's Guide
Expand ReferenceReference
  • Extreme Optimization
    • Features
    • Solutions
    • Documentation
    • QuickStart Samples
    • Sample Applications
    • Downloads
    • Technical Support
    • Download trial
    • How to buy
    • Blog
    • Company
    • Resources
  • Documentation
    • Introduction
    • Deployment Guide
    • Using Parallelism
    • Mathematics Library User's Guide
    • Vector and Matrix Library User's Guide
    • Statistics Library User's Guide
    • Reference
  • Reference
    • Extreme.Collections Namespace
    • Extreme.Mathematics Namespace
    • Extreme.Mathematics.Algorithms Namespace
    • Extreme.Mathematics.Calculus Namespace
    • Extreme.Mathematics.Calculus.OrdinaryDifferentialEquations Namespace
    • Extreme.Mathematics.Curves Namespace
    • Extreme.Mathematics.Curves.Nonlinear Namespace
    • Extreme.Mathematics.EquationSolvers Namespace
    • Extreme.Mathematics.Generic Namespace
    • Extreme.Mathematics.Generic.LinearAlgebra Namespace
    • Extreme.Mathematics.Generic.LinearAlgebra.Implementation Namespace
    • Extreme.Mathematics.Generic.LinearAlgebra.Providers Namespace
    • Extreme.Mathematics.Implementation Namespace
    • Extreme.Mathematics.LinearAlgebra Namespace
    • Extreme.Mathematics.LinearAlgebra.Complex Namespace
    • Extreme.Mathematics.LinearAlgebra.Complex.Decompositions Namespace
    • Extreme.Mathematics.LinearAlgebra.Implementation Namespace
    • Extreme.Mathematics.LinearAlgebra.IO Namespace
    • Extreme.Mathematics.LinearAlgebra.IterativeSolvers Namespace
    • Extreme.Mathematics.LinearAlgebra.IterativeSolvers.Preconditioners Namespace
    • Extreme.Mathematics.LinearAlgebra.Providers Namespace
    • Extreme.Mathematics.LinearAlgebra.Sparse Namespace
    • Extreme.Mathematics.Optimization Namespace
    • Extreme.Mathematics.Optimization.LinearProgramming Namespace
    • Extreme.Mathematics.Optimization.LineSearches Namespace
    • Extreme.Mathematics.SignalProcessing Namespace
    • Extreme.Mathematics.SpecialFunctions Namespace
    • Extreme.Statistics Namespace
    • Extreme.Statistics.Distributions Namespace
    • Extreme.Statistics.IO Namespace
    • Extreme.Statistics.Multivariate Namespace
    • Extreme.Statistics.Random Namespace
    • Extreme.Statistics.Tests Namespace
    • Extreme.Statistics.TimeSeriesAnalysis Namespace
  • Extreme.Mathematics.Calculus Namespace
    • AdaptiveIntegrator Class
    • AdaptiveIntegrator2D Class
    • AdaptiveIntegrator2DRule Enumeration
    • AdaptiveIntegrator3DRule Enumeration
    • AdaptiveIntegratorND Class
    • AdaptiveIntegratorNDRule Enumeration
    • DifferencesDirection Enumeration
    • GaussKronrodIntegrator Class
    • GaussKronrodIntegrator15 Class
    • GaussKronrodIntegrator21 Class
    • GaussKronrodIntegrator31 Class
    • GaussKronrodIntegrator41 Class
    • GaussKronrodIntegrator51 Class
    • GaussKronrodIntegrator61 Class
    • IntegrationRule Class
    • IntegrationRuleResult Structure
    • LeftPointIntegrator Class
    • MidpointIntegrator Class
    • NonAdaptiveGaussKronrodIntegrator Class
    • NumericalIntegrator Class
    • NumericalIntegrator2D Class
    • NumericalIntegratorND Class
    • Repeated1DIntegrator2D Class
    • Repeated1DIntegratorDirection Enumeration
    • RightPointIntegrator Class
    • RombergIntegrator Class
    • SimpsonIntegrator Class
    • TrapezoidIntegrator Class
  • MidpointIntegrator Class
    • Members
    • MidpointIntegrator Constructor
    • Methods
    • Properties
Collapse imageExpand ImageCopy imageCopyHover image
       




MidpointIntegrator Class

Members See Also 
Represents a numerical integrator that uses the mid-point rule.

Namespace: Extreme.Mathematics.Calculus
Assembly: Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 5.0.13017.0 (5.0.13248.0)

Syntax

C#
public sealed class MidpointIntegrator : NumericalIntegrator
Visual Basic
Public NotInheritable Class MidpointIntegrator
	Inherits NumericalIntegrator
Visual C++
public ref class MidpointIntegrator sealed : public NumericalIntegrator
F#
[<SealedAttribute>]
type MidpointIntegrator =  
    class
        inherit NumericalIntegrator
    end

Remarks

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.

Inheritance Hierarchy

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

Version Information

Numerical Libraries

Supported in: 5.0, 4.x, 3.6

See Also

MidpointIntegrator Members
Extreme.Mathematics.Calculus Namespace
Extreme.Mathematics.Calculus..::..TrapezoidIntegrator
Footer image

Send comments on this topic to support@extremeoptimization.com

Copyright (c) 2004-2013 ExoAnalytics Inc.

Copyright © 2003-2013, Extreme Optimization. All rights reserved.
Extreme Optimization, Complexity made simple, M#, and M Sharp are trademarks of ExoAnalytics Inc.
Microsoft, Visual C#, Visual Basic, Visual Studio, Visual Studio.NET, and the Optimized for Visual Studio logo
are registered trademarks of Microsoft Corporation.