Why does an iterative approach to solving a problem often work faster than a recursive method?

The iterative approach often works faster than the recursive one for several reasons:

1. No overhead of function calls. Each recursive call adds a new frame to the call stack, which takes time and memory.
2. Less memory consumption. Recursion uses the stack to store the state of each call, which can lead to stack overflow with deep recursion.
3. Compiler optimization. Iterative code is easier to optimize; the compiler can better parallelize and simplify the loop.

Example: calculating factorial

Recursively:

int factorial(int n) {
    if (n <= 1) return 1;
    return n * factorial(n - 1);
}

Iteratively:

int factorial(int n) {
    int result = 1;
    for (int i = 2; i <= n; ++i) {
        result *= i;
    }
    return result;
}

The iterative version is usually faster and safer for large n, as it does not involve deep recursive calls.