Divide and Average Method to Calculate Square Root

Hi, I am trying to write a function that uses the divide and average method to calculate a square root of both positive and negative numbers given a certain tolerance.

function estSqrt= ApproxSqrt(a,tol)
% function estSqrt= ApproxSqrt(a,tol)
if tol < 0
    disp('Your tolerance cannot be less than zero');
    return
end
if a < 0
    b = abs(a);
else
    b = a;
end
xOld= b/2;
%checkCon = true; 
while 1==1 %run until the if statement breaks the loop
    xNew = (xOld+a/xOld)/2;
    error = (xOld-xNew)/(xOld);
    xOld=xNew;
    if error<tol %test to see if the error is within acceptable bounds
        break %exit the while loop
    end
end
if a < 0
    estSqrt = xOld*1i;
    return
end
estSqrt = xNew;
end

However, if I try to use negative numbers, the code enters an infinite loop and does not return a value. Also, it returns incorrect value if the tolerance is higher (ie ApproxSqrt(1000000,0.5) should return 1027.65111408149323 but it instead returns 250001. Any help figuring this out would be greatly appreciated! Thanks!

Answer 1

[Steven Lord]

A couple comments about your while loop:

while 1==1 %run until the if statement breaks the loop

There are better ways to end the loop. See comment below.

    xNew = (xOld+a/xOld)/2;

You defined a variable b above the loop, but you're using a here. Should you be using b?

    error = (xOld-xNew)/(xOld);

There is a function named error in MATLAB, so I recommend avoiding using that name. Perhaps relativeError would be better? Also, do you care about the sign of the error or just its magnitude?

    xOld=xNew;
    if error<tol %test to see if the error is within acceptable bounds
        break %exit the while loop
    end

Rather than tucking your loop termination condition deep inside the loop, why not specify it at the beginning? While the error is greater than the termination tolerance ...

end