What's wrong with my bisection method function???

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Joe 2013-4-11

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https://ww2.mathworks.cn/matlabcentral/answers/71577-what-s-wrong-with-my-bisection-method-function

I'm not quite sure what's exactly wrong with my bisection method function that I have written. Can someone please help me figure out what the error is?

function root = bisectIter(f,a,b,tol)
if sign(f(a))==sign(f(b))
    error('a and b do not bracket the root');
end
k = 1;
x(k) = (a+b)/2;
while ((k<=tol)&&((b-a)/2)>= tol)
    if f(x(k)) == 0
        error('bisection condition didnt apply')
    end
    if (f(x(k))*f(a))<0
        b = x(k);
    else 
        a = x(k);
    end
    k = k + 1;
    x(k) = (a+b)/2;
    root = x(k);
end
end

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Matt J 2013-4-11

编辑：Matt J 2013-4-11

Show us what error you're getting and how to reproduce it.

Joe 2013-4-12

The error "Output argument 'root' not assigned during call..." shows up. I've already checked for the possible causes of this error and none seem to fit. When I alter my code so that it should produce an error when I run it, it does in fact produce that error instead of the output argument error.

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Answer 1

Roger Stafford 2013-4-12

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In the 'while' condition "((k<=tol)&&((b-a)/2)>= tol)" presumably you have set 'tol' to some very small number to allow a and b to approach each other closely. That means the "k<=tol" part will fail at the very beginning and you will never enter the while-loop. That is why the 'root' argument is never assigned.

In my opinion your 'while' criterion should be based on how close to zero the f function gets instead of the width b-a or the number of trips through the loop.

Also the "f(x(k)) == 0" condition that produces an error message is rather self-defeating. This is the very condition you are striving for, namely to find a root.