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
• Numerical recipes, The Art of Scientific Computing 3rd Edition, William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, 2007, isbn: 9780521880688
• Chapter 9 : Root finding an nonlinear sets of equations
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• teaching/methcalchim/root-finding_algorithm.txt
• Dernière modification: 2018/10/19 09:58
• de villersd