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teaching:methcalchim:root-finding_algorithm

Root findings : equations f(x) = 0

Algorithm used to find roots of an equation use iterations, and a numerical criterion to accept a solution when a sufficiently accurate value is reached. The rate of convergence depends on the used method and the function f(x). Some methods (Newton-Raphson) need the derivative of the function f(x).
  • Polynomial equations : Bairstow's method is an efficient algorithm for finding the roots of a real polynomial of arbitrary degree
  • Bisection method (dichotomy) : very simple and robust method, but relatively slow. It assumes continuity of the function, and obtain one roots. The algorithm is based on a loop invariant property : an interval [a, b] is said to bracket a root if f(a) and f(b) have opposite signs.
  • Secant method (retains the last two computed points)
  • Regula falsi (retains the points which preserve bracketing)
  • Chapter 9 in the book “Numerical Recipes” : Root finding an nonlinear sets of equations
    • 9.0 Introduction
    • 9.1 Bracketing and Bisection
    • 9.2 Secant Method, False Position Method, and Ridders' Method
    • 9.4 Newton-Raphson Method Using Derivative
    • 9.5 Roots of Polynomials
  • Python NumPy library : SciPy Reference

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teaching/methcalchim/root-finding_algorithm.txt · Dernière modification: 2018/10/19 09:58 par villersd