Matlab issue: Nested while loop paradox

I have an issue where I need to calculate x1, and keep calculating x1 until either the iterations reaches the desired number of iterations OR the approximate error in %(epsilon) is less than E(user defined tolerance in %).

My problem is that in order to calculate epsilon I must have the x1 value, but in order for the x1 value equation to be performed it must have the epsilon value to know when to end the while loop, so it's like there is a paradox. Any suggestions on how to solve this?

Answer 1

[Geoff Hayes]

Fraser - just initialize the error epsilon to some value that is greater then R so that the condition

 epsilon > E

is true and the body of the while loop will be evaluated. I think something like the following should work

 no_iter      = 0;
 epsilonError = 2*E;  % renamed to avoid confusion with built-in eps
 while no_iter < max_iter && epsilonError > E
     % calculate xinew

     % calculate epsilonError

     no_iter = no_iter + 1;
 end

Note that I've combined your two while loops into one because you need the two conditions together (as the calculated epsilon may never be less than E and so you will get stuck without the iteration count check).

Also, I am unclear on your calculation for xinew (what is xi?) and the purpose of the line

 if ((abs(xinew-xi)/xinew)*100)

which seems to have something to do with epsilonError.