Copyright | (c) 2011 Bryan O'Sullivan |
---|---|

License | BSD3 |

Maintainer | bos@serpentine.com |

Stability | experimental |

Portability | portable |

Safe Haskell | None |

Language | Haskell2010 |

Haskell functions for finding the roots of real functions of real arguments.

# Documentation

The result of searching for a root of a mathematical function.

NotBracketed | The function does not have opposite signs when evaluated at the lower and upper bounds of the search. |

SearchFailed | The search failed to converge to within the given error tolerance after the given number of iterations. |

Root a | A root was successfully found. |

:: a | Default value. |

-> Root a | Result of search for a root. |

-> a |

Returns either the result of a search for a root, or the default value if the search failed.

:: Double | Absolute error tolerance. |

-> (Double, Double) | Lower and upper bounds for the search. |

-> (Double -> Double) | Function to find the roots of. |

-> Root Double |

Use the method of Ridders to compute a root of a function.

The function must have opposite signs when evaluated at the lower and upper bounds of the search (i.e. the root must be bracketed).

:: Double | Required precision |

-> (Double, Double, Double) | (lower bound, initial guess, upper bound). Iterations will no go outside of the interval |

-> (Double -> (Double, Double)) | Function to finds roots. It returns pair of function value and its derivative |

-> Root Double |

Solve equation using Newton-Raphson iterations.

This method require both initial guess and bounds for root. If Newton step takes us out of bounds on root function reverts to bisection.

# References

- Ridders, C.F.J. (1979) A new algorithm for computing a single
root of a real continuous function.
*IEEE Transactions on Circuits and Systems*26:979–980.