i'm not sure what matlab is, but iterative means you check many values for a variable (your ). it's a guess and check thing. the difficulty is that is not necessarily an integer .

say you had the equation , and you knew what was. say in this case . a simple iterative method of finding the value of would be to replace with , then , then , and so on, until the value of is greater than ( ). in this case, we would find to be between and .

knowing that is not much of an answer, right? so now is when it gets a little harder.

at this point, you could do a binary search - which means you would guess , because that's right between and . so, , which is less than ( ). now you would guess right between and , so guess . is still less than , so you would guess between and , which is .... you would keep doing this until the error between and was minimal. you get to choose how much error is acceptable.

also, in the case of , you can get an answer algebraically, which is , however, in the case of your equation, i don't see an immediate algebraic solution. if you do find one, i would love to see it.

if this is confusing or if you would like more explanation about a binary search feel free to ask questions. a binary search is just one iterative method you might use, i'm sure you could find a better (faster) way.