Vector newton raphson method8/30/2023 % A threshold for distinguishing roots coming from different seeds. % Since sometimes we may not converge "max_iter" is set. % An array that keeps the number of required iterations. X0 = linspace(intrvl(1), intrvl(2), n_seeds) Bisection method).įunction = newton_raphson(fx, x, intrvl) % and to compare with other methods (e.g. This may be useful to find out the convergence rate % on the given interval and also the number of iterations to % returns "rt" a vector containing all of the roots for eq = 0 % 3) intrvl is the interval of interest to find the roots. % may input any string but it should be constructable as a "sym" object. % INPUT:1) "fx" is the equation string of the interest. % b) Newton's method implemented in MATLAB. XRoot = xNew %# Update the final value for the root XNew = subs(g,'x',xRoot) %# Update the new guess While abs(xNew-xRoot) > 1e-10 %# Loop while they differ by more than 1e-10 XNew = subs(g,'x',xRoot) %# Refined guess the root has been found): xRoot = 1 %# Initial guess You could also place the function evaluation in a while loop with a condition that checks how big a difference there is between each new guess and the previous guess, stopping when that difference is sufficiently small (i.e. You can see that the value of xRoot comes close to the value of the true root (which is 2) after just a couple of iterations. > xRoot = subs(g,'x',xRoot) %# Evaluate the function at the refined guess > xRoot = subs(g,'x',xRoot) %# Evaluate the function at the initial guess > g = x-f/diff(f) %# Create a Newton-Raphson approximation function > xRoot = 1 %# Initial guess for the root > f = (x-4)^2-4 %# Create a function of x to find a root of Here's an example of finding a root using the Newton-Raphson method: > syms x %# Create a symbolic variable x What you're probably wanting to do is differentiation of symbolic equations, and you need the Symbolic Math Toolbox for that. You would have to do this numerically by evaluating the function at a number of points and approximating the derivative. There's no way to algebraically take derivatives of function handles or functions defined in m-files.
0 Comments
Leave a Reply.AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |