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teaching:methcalchim:root-finding_algorithm [2018/10/19 09:37]
villersd créée
teaching:methcalchim:root-finding_algorithm [2018/10/19 09:58] (Version actuelle)
villersd
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 ====== Root findings : equations f(x) = 0 ====== ====== Root findings : equations f(x) = 0 ======
  
 +<note tip>
 +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).
 +</​note>​
  
   * Polynomial equations : [[wp>​Bairstow'​s_method|Bairstow'​s method]] is an efficient algorithm for finding the roots of a real polynomial of arbitrary degree   * Polynomial equations : [[wp>​Bairstow'​s_method|Bairstow'​s method]] is an efficient algorithm for finding the roots of a real polynomial of arbitrary degree
Ligne 9: Ligne 12:
   * [[wp>​False_position_method|Regula falsi]] (retains the points which preserve bracketing)   * [[wp>​False_position_method|Regula falsi]] (retains the points which preserve bracketing)
   * [[wp>​Newton'​s_method|Newton-Raphson method]]   * [[wp>​Newton'​s_method|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 [[https://​docs.scipy.org/​doc/​numpy/​|NumPy]] library : [[https://​docs.scipy.org/​doc/​scipy/​reference/​|SciPy Reference]]
 +    * [[https://​docs.scipy.org/​doc/​scipy/​reference/​tutorial/​optimize.html|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 ​
teaching/methcalchim/root-finding_algorithm.txt · Dernière modification: 2018/10/19 09:58 par villersd