Do iterative and recursive versions of an algorithm have the same time complexity?

Question

Say, for example, the iterative and recursive versions of the Fibonacci series. Do they have the same time complexity?

Answer 1

Yes, every iterative algorithm can be transformed into recursive version and vice versa. One way by passing continuations and the other by implementing stack structure. This is done without increase in time complexity.

If you can optimize tail-recursion then every iterative algorithm can be transformed to recursive one without increasing asymptotic memory complexity.