MATLAB: How to find positive x-root of this function

root estimation

Hi All,
I want to find positive root x of this function;
x^10=1;
I wrote a program using modified false postion algorythm but i don't know how to use it to solve equation written above. Here is the Code;
function ModFalsePos=eqn(xl,xu,es,xr,ea)
f=@(x)x^10-1
xl=0
xu=1.3
es=0.01
fl=f(xl)
fu=f(xu)
while (1)
    xr=xu-fu*(xl-xu)/(fl-fu)
    xrold=xr
    fr=f(xr)
    if xr<0
    elseif xr>0
        ea=abs((xr-xold)/xr)*100
    end
    test=fl*fr
    if test<0
        xu=xr
        fu=f(xu)
        iu=0
        il=il+1
        if il>=2
            fl=fl/2
        end
    elseif test>0
        xl=xr
        fl=f(xl)
        il=0
        iu=iu+1
        if iu>=2
            fu=fu/2
        end
    else
        ea=0
    end
    if ea<es
        break
    end
end
ModFalsePos=xr
end
Could anyone please help me for solving this equation using this code? What's wrong here?
Thanks for any Help!

Best Answer

Okay, in this line here:
ea=abs((xr-xold)/xr)*100
ea is always going to be zero, since a few lines above, you assigned xold=xr. Thus your algorithm always exits after the first iteration. So you need to flip the first lines after while:
    xrold = xr;
    xr = xu - fu*(xl-xu)/(fl-fu);
Then, you need to initialize iu, il and xr outside of the loop.
xu=1.3;
xr=xu;
iu = 0; il = 0;
Also, remove the function line and the last end, what you have here is a script, not a function. If you want it to be a function, at least f should be an input argument, too, otherwise it doesn't make much sense.
And now it should be running.
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