newton raphson in matlab

To implement the Newton-Raphson method in MATLAB, you can follow these steps:

  1. Define the function f(x) for which you want to find the root.
  2. Define the derivative of the function f'(x).
  3. Choose an initial guess value for the root, let's say x0.
  4. Iterate the following steps until the desired level of accuracy is achieved:
    • Calculate the next approximation of the root using the formula: x = x0 - f(x0)/f'(x0)
    • Update the value of x0 with the new approximation.
    • Repeat until the difference between consecutive approximations is below a given tolerance level.

Here's an example code that implements the Newton-Raphson method in MATLAB:

main.m
function root = newtonRaphson(f, df, x0, tolerance, maxIterations)
    % f: function handle for f(x)
    % df: function handle for f'(x)
    % x0: initial guess for the root
    % tolerance: desired level of accuracy
    % maxIterations: maximum number of iterations allowed
    
    % Initialize variables
    x = x0;
    iteration = 0;
    error = Inf;
    
    % Iterate until the desired level of accuracy or maximum iterations are reached
    while error > tolerance && iteration < maxIterations
        xPrev = x;
        x = xPrev - f(xPrev) / df(xPrev);
        error = abs(x - xPrev);
        iteration = iteration + 1;
    end
    
    % Check if the method converged or not
    if error > tolerance
        fprintf('The method did not converge after %d iterations.\n', maxIterations);
        root = NaN;
    else
        fprintf('Root found after %d iterations.\n', iteration);
        root = x;
    end
end

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To use the above function, you need to define your function f(x) and its derivative f'(x) separately. For example, let's say you want to find the square root of a number n. You can define f(x) = x^2 - n and its derivative f'(x) = 2*x. Then, you can call the newtonRaphson function as follows:

main.m
f = @(x) x^2 - n;    % Define f(x)
df = @(x) 2*x;       % Define f'(x)
x0 = 1;              % Initial guess
tolerance = 1e-6;    % Tolerance level
maxIterations = 100; % Maximum number of iterations
root = newtonRaphson(f, df, x0, tolerance, maxIterations); % Call the function
disp(root);          % Display the root

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Ensure that you replace n with the desired number for which you want to find the square root.

Make sure to test your implementation with different functions and initial guess values to ensure its correctness.

Hope this helps!

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matlab
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