Root = newton_raphson(f, df, x0, tol, max_iter) Īfter running this code, the variable ‘ root‘ will contain the approximated root of the function ‘ f(x)‘. For example, if we want to find the root of ‘ f(x) = x^2 - 2‘ starting from an initial guess of ‘ x0 = 1‘, with a tolerance of ‘ tol = 1e-6‘, and a maximum of ‘ max_iter = 100‘ iterations, we would call the function like this: f = x^2 - 2 To use this function, you would define your function ‘ f(x)‘ and it’s derivative ‘ df(x)‘, specify an initial guess ‘ x0‘, a tolerance ‘ tol‘, and a maximum number of iterations ‘ max_iter‘. % Check if the maximum number of iterations was reached without achieving desired level of accuracyĭisp('Maximum iterations reached without finding a root within tolerance.') % Compute the next approximation using the Newton-Raphson formula % Loop until the desired level of accuracy is achieved or maximum iterations reached % Initialize x_n to be the initial guess x0 % x: the approximated root of the function f(x)

% max_iter: the maximum number of iterations % tol: the tolerance for the root (i.e., how close x_n is to the actual root) Newton-Raphson Method in Matlab Ask Question Asked 9 years, 1 month ago Modified 3 years, 11 months ago Viewed 42k times 4 I am new to matlab and I need to create a function that does n iterations of the Newton-Raphson method with starting approximation x a. % df: the derivative of the function f(x) % Newton-Raphson method for finding the root of a function f(x) Here is an example implementation for finding the root of a function ‘ f(x)‘: function x = newton_raphson(f, df, x0, tol, max_iter) In MATLAB, you can implement the Newton-Raphson method using a loop that iteratively applies the formula described above. It is used for solving equations that cannot be solved analytically, such as finding the roots of a polynomial or a transcendental equation. The method has many applications in various fields, including physics, engineering, finance, and computer science. The method may converge to a root or diverge to infinity, depending on the function and the initial guess. To use the method, one starts with an initial guess x_0 and applies the above formula to generate successive approximations ‘ x_1‘, ‘ x_2‘, ‘ x_3‘, and so on, until the desired level of accuracy is achieved. Where ‘ x_n‘ is the current approximation of the root, ‘ f(x_n)‘ is the function evaluated at ‘ x_n‘, and ‘ f'(x_n)‘ is the derivative of the function evaluated at ‘ x_n‘. The method is based on the following iterative formula: x_ = x_n - f(x_n) / f'(x_n) It is an iterative method that starts with an initial guess of the root and refines the guess with each iteration until the desired level of accuracy is achieved. The Newton-Raphson method is a numerical method used for finding the roots of a differentiable function.

Code matlab of newton raphson method