NMath Reference Guide

## Romberg |

Class RombergIntegrator approximates integrals of functions over a
given interval using the Romberg method.

Inheritance Hierarchy

Syntax

The RombergIntegrator type exposes the following members.

Constructors

Name | Description | |
---|---|---|

RombergIntegrator | Default constructor. Constructs a RombergIntegrator instance with default tolerance and default maximum order. | |

RombergIntegrator(Double) | Constructs a RombergIntegrator instance with the given error tolerance and default maximum order. | |

RombergIntegrator(Int32) | Constructs a RombergIntegrator instance with the given maximum order and default error tolerance. | |

RombergIntegrator(Double, Int32) | Constructs a RombergIntegrator instance with the given error tolerance and maximum order. |

Properties

Name | Description | |
---|---|---|

DefaultMaxOrder | Gets and sets the default maximum order for instances of RombergIntegrator. | |

DefaultTolerance | Gets and dets the default error tolerance for instances of RombergIntegrator. | |

MaximumOrder | Gets and sets the maximum order used in computing Romberg estimates. | |

Order | Gets the order of the Romberg approximation. | |

RombergErrorEstimate | Gets an estimate of the error in the Romberg estimate of the integral just computed. | |

RombergEstimate | Gets the Romberg estimate for the integral. | |

SimpsonEstimate | Gets the estimate for the integral yielded by the compound Simpson's rule where the number of panels, or subintervals, is equal to the order of the Romberg estimate. | |

Tableau | Gets a matrix of successive approximations computed while computing a Romberg estimate. | |

Tolerance | Gets and sets the error tolerance used in computing Romberg estimates. | |

ToleranceMet | Returns true if the Romberg estimate just computed stopped because the error tolerance was reached; otherwise, false. | |

TrapezoidEstimate | Gets the estimate for the integral yielded by the compound trapezoid rule where the number of panels, or subintervals, is equal to the order of the Romberg estimate. |

Methods

Name | Description | |
---|---|---|

Clone | Creates a deep copy of this integrator. | |

Integrate(OneVariableFunction, Double, Double) | Estimates the integral of the given function over the given interval. | |

Integrate(DoubleVector, DoubleVector, Double, Double) | Estimates the integral of a linearly interpolated function between the points. |

Remarks

Instances of RombergIntegrator can configured to compute
successive Romberg approximations of increasing order until the
estimated error in the approximation is less than a specified tolerance,
or until a maximum order is reached. To compute a Romberg estimate of a
specific order, k, set the MaximumOrder property to k and the
tolerance to a negative value.

See Also