Common Numerical Root Finding Methods |

Common root finding schemes for functions with one independent variable are briefly discussed in this section. They include: |

Bisection Method |

The idea of the When an interval contains a root, the bisection method is the one that |

Secant Method | ||

To improve the slow convergence of the bisection method, the
Mathematically, the secant method converges more rapidly near a root than the false position method (discussed below). However, since the secant method does not always bracket the root, the algorithm |

False Position Method |

Similar to the secant method, the false position method also uses a straight line to approximate the function in the local region of interest. The only difference between these two methods is that the secant method keeps the most recent two estimates, while the false position method retains the most recent estimate and the next recent one which has an opposite sign in the function value. The false position method, which sometimes keeps an older reference point to maintain an opposite sign bracket around the root, has a lower and uncertain convergence rate compared to the secant method. The emphasis on bracketing the root may sometimes restrict the false position method in difficult situations while solving highly nonlinear equations. |

Newton-Raphson Method | ||

The Newton-Raphson method finds the slope (the tangent line) of the function at the current point and uses the zero of the tangent line as the next reference point. The process is repeated until the root is found.
The Newton-Raphson method is much more |