The code you have so far will require a number of revisions before it gives the desired result. The principal issue is that the equations in the loop are implemented too literally with not enough regard for the Matlab syntax.
A first step would be to define our target function more explicitly:
function y = f(x)
y = x^3 - x^2 - 4*x + 1;
end
And I assume you are expected to find the derivative manually. The diff function is not going to serve properly here. You could define it to be used conveniently in the algorithm:
function y = f_prime(x)
% differentiate the polynomial
y =
end
Regarding the primary function root_newton, is the expected output of root_newton(2) the result of the algorithm with x0 = 2? In such a case, it would be reasonable to proceed:
% calling the return value 'y' is arbitrary. There's usually a name that is
% more descriptive and convenient
function x_n = root_newton(x_0)
x_n = x_0; % establish the initial condition of the algorithm (together with the above functions)
while abs(f(x_n)) > 0.0001
x_n = ...
end
end
Here, the loop condition abs(f(x_n)) is indeed equivalent to your code, but the intention is more direct. The final step is to fix the iteration. When implementing interative and recursive style algorithms, generally there is no reference to an "n+1", you just need to directly update the x_n variable with the equation for the next iteration. The nested for loop is superfluous. The iteration count n is essentially determined by the threshold which is set at 0.0001 and ultimately is not worth keeping track of unless specifically called for.
