matlab编程应用Newton迭代法求方程x3-x-1=0在x=1附近的数值解xk，并使其满足|xk-xk-1|＜10-8给出完整代码 给出迭代次数 和时间

Sure, I can help you with that. Here's a MATLAB code snippet that uses the Newton-Raphson method to find the root of the equation `f(x) = x^3 - x - 1` near `x = 1`. The code will stop iterating when the difference between consecutive approximations is less than `1e-8`.

% Define the function and its derivative (using symbolic math)
syms x
f = x^3 - x - 1;
df = diff(f);

% Set initial guess
x0 = 1;
tol = 1e-8; % Tolerance for convergence

% Initialize variables
iter_count = 0;
start_time = tic;

% Newton-Raphson iteration loop
while true
    iter_count = iter_count + 1;
    
    % Compute the next approximation
    xk = x0 - f(x0) / df(x0);
    
    % Check for convergence
    if abs(xk - x0) < tol
        break;
    end
    
    % Update the previous approximation
    x0 = xk;
end

% Calculate the time taken
elapsed_time = toc(start_time);
approximation = xk;
iterations = iter_count;

disp(['Solution: ' num2str(approximation)]);
fprintf('Iterations: %d\n', iterations);
fprintf('Elapsed Time: %f seconds\n', elapsed_time);

This code defines the function and its derivative symbolically, sets an initial guess, and then performs the iterative process until the tolerance condition is met. It also calculates the number of iterations and the time taken.

To run this code, copy it into a `.m` file in your MATLAB workspace, and execute it by typing `run('filename.m')`, replacing `filename` with the name of your file.