MATLAB: HELP! Bisection method fails to found zero

Question

I tried to calculate the zero for the function , but the zero isn't found in . I have the same problem for other function like .

I paste here my code (part of my function) :

TOLF = eps;
nit= 0; % number of iterations
m = xo(1)+0.5*diff(xo); % midpoint
while(abs(diff(xo))> p.Results.TOL*max(abs(xo)) && ...
        abs(fun(m))>TOLF && nit<p.Results.NMAX) % stopping condition
    if(fun(m)*fun(xo(1))<0)
        xo(2)= m;
    else
        xo(1)= m;
    end
    nit=nit+1;
    m = xo(1)+0.5*diff(xo);
end

Answer 1

Simply use the debugger to test, what's going on:

https://www.mathworks.com/help/matlab/matlab_prog/debugging-process-and-features.html

You can check programmatically also, why the loop is stoped:

ready = false;
while ~ready
    ...
    readyTOL = (abs(diff(xo)) >= TOLX;
    readyABS = abs(fun(m)) >= TOLF;
    readyNIT = nit<p.Results.NMAX;
    ready    = (readyTOL || readyABS || readINT);
end
output.stopped = [readyTOL, readyABS, readINT];
...

Now you can see, which condition has stopped the loop.

By the way, this test is not useful:

if (abs(diff(xo))> p.Results.TOL*max(abs(xo)) && ...
        abs(fun(m))>TOLF && ...
        nit==p.Results.NMAX)
    warning("limit reached... calculation stopped!");
end

It is very unlikly, that the maximum iteration number was reached and the absolute tolerance and the relative tolerance for the interval length at the same time.

I assume you want this:

if nit == p.Results.NMAX
    warning("Maximum number of iterations reached!");
end

This warns, if the found solution is not accurate, because the process stopped by the iteration counter.

What about replacing:

    if(max(abs(xo))>realmin/p.Results.TOL)
        TOLX = p.Results.TOL * max(abs(xo));
    else
        TOLX = realmin;
    end

by

TOLX = max(p.Results.TOL * mmax(abs(xo)), realmin);