Assume for simplicity $C_1,C_2,...,C_n\subset \mathbb{R}^n$ to be closed and convex subsets with $\underset{i=1}{\overset{n}{\bigcap{}}}C_i\neq\emptyset$.

Let $x^0\in\mathbb{R}^n$ and define the following iterative method:
$$x^{k+1}=P_{C_{i_k}}(x^k)$$
Where $P_{C_{i_k}}$ is the projection onto the set $C_{i_k}$ and $i_k:\mathbb{N}\cup\{0\}\rightarrow\{1,...,n\}$ is the control sequence.

I would like to ask the following two questions:

**Q1**: The special case of $n=2$ is fairly well understood and an exact rate of convergence is known, see for example [this paper][1]. Is a similar result known for more than two subsets, perhaps with additional assumptions?

**Q2**: Some control sequences can be demonstrated numerically to be faster than others in terms of iterations, for example, the _cyclic control_: $$i_k=(k\mod n)+1$$  can be shown to be slower than the _remotest set control_: $$i_k=\underset{i\in\{1..n\}}{argmax}\:d(x^k,C_i)$$ Are there papers that capture this behavior theoretically?


  [1]: http://www.mathnet.ru/links/e13e2cf9e71df195d082d2e338511d94/aa1241.pdf