NMath Reference Guide

## Brent |

Class BrentMinimizer uses Brent's Method to minimize a function within an interval
known to contain a minimum.

Inheritance Hierarchy

Syntax

The BrentMinimizer type exposes the following members.

Constructors

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

BrentMinimizer | Default constructor. | |

BrentMinimizer(Double) | Constructs a BrentMinimizer instance with the given error tolerance. | |

BrentMinimizer(Int32) | Constructs a BrentMinimizer instance with the given maximum number of iterations. | |

BrentMinimizer(Double, Int32) | Constructs a BrentMinimizer instance with the given error tolerance and maximum number of iterations. |

Properties

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

Error |
Gets the error associated with the mimimum just computed.
(Inherited from MinimizerBase) | |

Iterations |
Gets the number of iterations used in the estimate of the mimimum
just computed.
(Inherited from MinimizerBase) | |

MaxIterations |
Gets and sets the maximum number of iterations used in computing minima
estimates.
(Inherited from MinimizerBase) | |

MaxIterationsMet |
Returns true if the minimum just computed stopped because the
maximum number of iterations was reached; otherwise, false.
(Inherited from MinimizerBase) | |

Tolerance |
Gets and sets the error tolerance used in computing minima estimates.
(Inherited from MinimizerBase) | |

ToleranceMet |
Returns true if the minimum just computed stopped because the
error tolerance was reached; otherwise, false.
(Inherited from MinimizerBase) |

Methods

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

Clone |
Creates a deep copy of self.
(Overrides MinimizerBaseClone) | |

Minimize(Bracket) | Minimizes the function within the interval contained in the given Bracket. | |

Minimize(OneVariableFunction, Interval) | Minimizes the given function within the given interval. | |

Minimize(OneVariableFunction, Double, Double) | Minimizes the given function within the given interval. | |

Minimize(OneVariableFunction, Double, Double, Double) | Minimizes the given function within the given interval. |

Fields

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

error_ | The current error. (Inherited from MinimizerBase) | |

iter_ | The current number of iterations performed. (Inherited from MinimizerBase) | |

max_ | The maximum number of iterations. (Inherited from MinimizerBase) | |

tolerance_ | The error tolerance. (Inherited from MinimizerBase) |

Remarks

Brent's Method combines golden section search (see class GoldenMinimizer)
with parabolic interpolation. Parabolic interpolation fits a parabola through the current
set of points, then uses the parabola to estimate the function's minimum.
Iteration stops when either the estimated error is less than a specified error
tolerance, or a specified maximum number of iterations is reached.

The faster parabolic interpolation is used wherever possible, but in steps where the projected minimum falls outside the interval, or when successive steps are becoming larger, Brent's Method resorts back to the slower golden section search. Brent's Method is quadratically convergent, rather than linearly convergent like the golden section search.

The faster parabolic interpolation is used wherever possible, but in steps where the projected minimum falls outside the interval, or when successive steps are becoming larger, Brent's Method resorts back to the slower golden section search. Brent's Method is quadratically convergent, rather than linearly convergent like the golden section search.

See Also