Newton-Raphson Method in MATLAB for f(x)=tan-1 (x-1) - 0.5

[roam]

In MATLAB, I want to use the Newton-Raphson method with absolute tolerance 1e-1, other tolerances zero, and an initial estimate x0 = 4 to find a zero of the function

f(x) = tan^-1 (x-1) - 0.5

And then repeat the process for a better estimate with absolute tolerance 10^-9. So here is my code so far:

format long
x=4;
ind=0;
k=1;
f=@(x)(atan(x-1)-0.5);
fp=@(x)(1/((x - 1)^2 + 1));
N=30;
tola=1e-1;
tolr=0;
tolf=0;
 
while ind == 0 & k <= N,
    fp_value=feval(fp,x);
    if fp_value ~= 0,
        f_value=feval(f,x);
        if abs(f_value)>tolf,
            x_new=x - f_value/fp_value;
            if abs(x_new - x)<= tola + tolr * abs(x),
                ind=2;
            end
            x=x_new;
        else
            ind=1;
        end
    else
        ind=3;
    end
    k=k+1;
end
 
if ind==0,
    ind=4;
end
 
x

But we get:

x =
 
   -2.742845125833007e+211

So why is it that we don't get a single number instead of all 30 iterations?

Also when I changed the value of the absolute tolerance to 10^-9, there was no change in the output. Why is that? I'm new to Matlab, so any help is greatly appreciated.

 

[DrClaude]

To get intermediate values, remove the ; in the line

x=x_new;

Since the wrong result is obtained, the tolerance is never reached, which is why its value is irrelevant. The problem is that the initial guess is too far from the real solution.