Newton's method in Matlab

I am trying to apply Newton's method in Matlab, and I wrote a script:

syms f(x)
f(x) = x^2-4
g = diff(f)

x_1=1 %initial point

while f(['x_' num2str(i+1)])<0.001;% tolerance
    
    for i=1:1000 %it should be stopped when tolerance is reached
       
        ['x_' num2str(i+1)]=['x_' num2str(i)]-f(['x_' num2str(i)])/g(['x_' num2str(i)])
    
    end

end

I am getting this error:

 Error: An array for multiple LHS assignment cannot contain M_STRING.

Newton's Method formula is x_(n+1)= x_n-f(x_n)/df(x_n) that goes until f(x_n) value gets closer to zero.

[John D'Errico]

You should realize that things like this:

['x_' num2str(i+1)]=['x_' num2str(i)]-f(['x_' num2str(i)])/g(['x_' num2str(i)])

are not valid MATLAB syntax, that you cannot create or access variables on the fly like that.

Answer 1

[Basil C.]

You seem to have made some fudamentals errors in your code.

1. the variable 'x' cannot be used however you feel right

2. also with the for loop in your code would have to run for 1000 iteration every time which makes it inefficient so always put a condition inside it

Please use the below code....

syms f(x) x
f(x) = x^2-4;
g = diff(f);

x(1)=1 ;%initial point

for i=1:1000 %it should be stopped when tolerance is reached
        x(i+1) = x(i) - f(x(i))/g(x(i));
        if( abs(f(x(i+1)))<0.001)   % tolerance
            disp(double(x(i+1)));
            break;
       end
end

[Lee Kruse]

Your code example doesn't work for me. Gives an error at the if statement "Conversion to logical from sym is not possible."

[Anurag Harsh]

same here

[Sergio E. Obando]

Basil's code works for me on R2024a. For an alternate solution that does not rely on symbolic variables, you can try this:

f = @(X) X.^2 - 4;
dfdx = @(X) 2*X;

nIter = 1000;
tol = 0.001;

x = zeros(1,nIter);
x(1) = 1;

for ii = 1:nIter
    
    x(ii+1) = x(ii) - f(x(ii))/dfdx(x(ii));
    if abs(f(x(ii+1))) < tol
        disp(x(ii+1));
        break
    end
end

    2.0000