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
- Polynomials in NumPy
- polynomial module, including polyroots(c) to compute the roots of a polynomial.
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)
Newton-Raphson method
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
- scipy.optimize package (root)

Applications

Références

Numerical recipes, The Art of Scientific Computing 3rd Edition, William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, 2007, isbn: 9780521880688
- http://numerical.recipes/
  - in C : http://apps.nrbook.com/c/index.html
- http://www2.units.it/ipl/students_area/imm2/files/Numerical_Recipes.pdf, p 347…
- http://apps.nrbook.com/empanel/index.html#
  - Chapter 9 : Root finding an nonlinear sets of equations