MATLAB: Is the newton method giving me a huge answer? What am i doing wrong?pls help

MATLABnewton method

x= sym('x');
p = 0.6;
F = x^5+4*x^2-1;
F_prime = diff(F);
N=0;
q = p - subs(F,x,p)/subs(F_prime,x,p);
while(N < 100 && not(abs(p-q) <= .00001 ))
        N=N+1;
        p = q;
        q = p - ((subs(F,x,p))./(subs(F_prime,x,p)));
        
end 
if(N == 100)
    print("Too many iterations");
else
    display(q)
end

Best Answer

When you have a problem like this, plot the function. In fact, plot the function anyway!
Next, it is a bad idea to use variables like p and q, then swaping them back and forth. Use variable names that make sense!!!!!
Next, don't keep things symbolic. That causes problems, because you don't know how to work with symbolic variables that well. Use functions instead.
I'll start with a symbolic function, then differentiate it in symbolic form. But then alllow matlabFunction to convert it to a function handle.
Finally, I cleaned up the logic in your code.
x = sym('x');
xcurrent = 0.5; % start point
xold = inf; % the first time through, you need to pass the while condition
F = x^3+4*x^2-10;
F_fun = matlabFunction(F);
fplot(F_fun)
hold on
plot(xcurrent,F_fun(xcurrent),'o')
F_prime = matlabFunction(diff(F));
N=0;
tolerance = 1.e-6;
while (N < 30) && (abs(xcurrent-xold) > tolerance )
    N=N+1;
    xold = xcurrent;
    xcurrent = xold - F_fun(xold)./F_prime(xold);
    
    plot(xcurrent,F_fun(xcurrent),'o')
end 
if(N == 30)
    print("Too many iterations");
else
    display(xcurrent)
end
That should get the point across, that there is no need to use symbolic tools as heavily as you are.
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