How much extra memory does garbage collection require?

Question

I heard once that for a language to implement and run garbage collection correctly there is on average of 3x more memory required. I am not sure if this is assuming the

Answer 1

According to the 2005 study Quantifying the Performance of Garbage Collection vs. Explicit Memory Management (PDF), generational garbage collectors need 5 times the memory to achieve equal performance. The emphasis below is mine:

We compare explicit memory management to both copying and non-copying garbage collectors across a range of benchmarks, and include real (non-simulated) runs that validate our results. These results quantify the time-space tradeoff of garbage collection: with five times as much memory, an Appel-style generational garbage collector with a non-copying mature space matches the performance of explicit memory management. With only three times as much memory, it runs on average 17% slower than explicit memory management. However, with only twice as much memory, garbage collection degrades performance by nearly 70%. When physical memory is scarce, paging causes garbage collection to run an order of magnitude slower than explicit memory management.