My loop has an infinite recursion, and I'm not sure how to fix it?

I'm trying to implement the Babylonian method through a while loop. When I call my function in another script file, it says I have an infinite recursion. I think it has something to do with my boundary variable. I'm not quite sure how to fix it.

function y = divide_and_average(initialGuess,a,limit)

   y = (initialGuess + a/(initialGuess))/2; %calculation for square
   boundary = (abs(y-initialGuess)/y); % compare the limit to

while boundary > limit %will continue until false
    y = initialGuess;
    divide_and_average(y,a,limit);
    boundary = (abs(y-initialGuess)/y);
end

Answer 1

[Brendan Hamm]

You always set y to be the initial guess and call divide_and_average with y which is the initial guess.

while boundary > limit %will continue until false
    y = initialGuess; % y is set to your initialGuess
    % Now we call this function with the exact inputs it was originally called with. This happens infinitely.
    divide_and_average(y,a,limit); 
    boundary = (abs(y-initialGuess)/y);
end

[Brendan Hamm]

It seems you likely want to remove the line,

y = initialGuess

and rather you want the next call to happen with:

y = (initialGuess + a/(initialGuess))/2;

[Maryam Ansari]

So I made some modifications to my code:

function y = divide_and_average(initialGuess,a,limit)

   y = (initialGuess + a/(initialGuess))/2; %calculation for square
   boundary = (abs(y-initialGuess)/y); % compare the limit to
   square = 0;

while boundary > limit %will continue until false
    square = divide_and_average(y,a,limit);
    y = square; %%replacing y value with square to converge to root
    boundary = (abs(y-initialGuess)/y); %%using changed y value
end

display(square);

however, the while loop doesn't stop. I think this has something to do with my boundary variable? Does it not change in the loop?

[Maryam Ansari]

So I actually fixed my boundary. However, my condition isn't fulfilled.

function y = divide_and_average(initialGuess,a)

   y = (initialGuess + a/(initialGuess))/2; %calculation for square
   boundary = (abs(y-initialGuess)/y); % compare the limit to
   square = 1;

while boundary >= 10^-6 %will continue until false
    square = y; %%calls function with y as initial guess
    boundary = (abs(square-initialGuess)/square); %%changes boundary until it is less than the limit
    initialGuess = square; %%replaces initialGuess with value calculated above to converge to root  
end

display(square);

the answer I get when I call my function divide_and_average(3.9,16) is 4.0013, which isn't within 10^-6 of the actual square root of 16

[Brendan Hamm]

In your while loop square takes on the value of y on every iteration but y does not change. Also, your calculation of the boundary is not correct.

function [y,error] = divide_and_average(initialGuess,a,limit)
    % Calculate square based on initial guess, this is our new guess
    y = (initialGuess + a/(initialGuess))/2; 
    error = (a - y^2)/(2*y); % This is the approximate error in the answer
while abs(error) >= limit %will continue until false
    % Call the function with our new "initialGuess" and get the
    % corresponding error.
    [y,error] = divide_and_average(y,a,limit); 
end

This is now within the appropriate tolerance:

format long
[square,err] = divide_and_average(3.9,16,1e-6)
square =
 4.000000205391106
err =
  -2.053911006834815e-07

[Brendan Hamm]

I highly suggest taking a look at the MATLAB Debugging options which will allow you to determine where error in your code are.