iteration newton raphson

Question

sukhraj Randhawa 2012-3-21

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/32988-iteration-newton-raphson

回答： Rahul 2024-8-26

i am having difficulty trying to find an iteration formula using newton-raphson for solving the equation x=cos(2x) and write an m-file for finding the solution whereby x matches cos(2x) to atleast 8 decimal places using format long. can anybody help me?

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

arushi 2024-8-26

在 MATLAB Online 中打开

Hi Sukhraj,

Here is the one example of implemtention for your reference:

function x = solve_cos2x()
    % Initial guess
    x = 0.5; % You might need to adjust this based on the problem
    tolerance = 1e-8;
    maxIterations = 1000;
    iteration = 0;
    
    while true
        % Calculate the function and its derivative
        fx = x - cos(2 * x);
        dfx = 1 + 2 * sin(2 * x);
        
        % Newton-Raphson update
        x_new = x - fx / dfx;
        
        % Check for convergence
        if abs(x_new - x) < tolerance
            break;
        end
        
        % Update x
        x = x_new;
        
        % Increment iteration count
        iteration = iteration + 1;
        if iteration >= maxIterations
            warning('Maximum iterations reached without convergence.');
            break;
        end
    end
end

Hope this helps.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Rahul 2024-8-26

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/32988-iteration-newton-raphson#answer_1505199

在 MATLAB Online 中打开

Hi @sukhraj Randhawa,

I understand that you are trying to find an iteration formula using Newton-Raphson for solving the equation x=cos(2x) where x matches cos(2x) to atleast 8 decimal places using format long.

As similarly mentioned by @arushi, you can use a loop for iterating through the values and update the variables using the Newton-Raphson method. An example is as follows:

format long % Initially set the format as long
x_solution = solve_cos_2x();
function x = solve_cos_2x()
   
    syms z % Setting this to get equations
    fx = z - cos(2*z);
    diff_fx = diff(fx);
    
    x = 0.5; % You can choose a different starting point if needed
    tol = 1e-8; 
    max_iter = 100; % You can adjust max iters
    
    for iter = 1:max_iter
        
        % Newton-Raphson update
        x_next = x - double(subs(fx, z, x)) / double(subs(diff_fx, z, x));
        
        if abs(x_next - x) < tol
            break;
        end
        x = x_next;
    end
    
    if iter == max_iter
        warning('Maximum number of iterations reached without convergence.');
    else
        fprintf('Converged to x = %.10f in %d iterations\n', x, iter);
    end
end