two non-linear equatio newton raphson method in matlab

main.m
% Define the non-linear equations as separate functions
f1 = @(x, y) x^2 - y - 1;
f2 = @(x, y) x + y^2 - 4;

% Set the initial guess for the roots
x0 = 0;
y0 = 0;

% Set the desired level of accuracy
tolerance = 1e-6;

% Initialize the error
error = inf;

% Initialize the iteration counter
iter = 0;

% Iterate the Newton-Raphson method until the desired level of accuracy is reached
while error > tolerance
    % Evaluate the functions and their partial derivatives at the current guess
    F = [f1(x0, y0); f2(x0, y0)];
    J = [2*x0, -1; 1, 2*y0];
    
    % Calculate the step size using matrix inversion
    delta = -J\F;
    
    % Update the guess
    x = x0 + delta(1);
    y = y0 + delta(2);
    
    % Update the error and iteration counter
    error = norm([x; y] - [x0; y0]);
    iter = iter + 1;
    
    % Update the previous guess
    x0 = x;
    y0 = y;
end

% Return the final estimates of the roots
root1 = x;
root2 = y;
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