I would like to solve a Least Squares (LS) problem of the form y=Fx. Let's assume for simplicity that $y \in \mathbb{R}^{2N}$ vector, $F= \left[ \begin{array}{cc} F_1 & 0 \\ 0 & F_2 \end{array} \right] \in \mathbb{R}^{2N \times 2p}$ with each $F_i\in \mathbb{R}^{N \times p}$ and $x\in \mathbb{R}^{2p}$.
I am using Matlab and I would like to discuss in general about this kind of problems.
1) Is it faster to break the problem in separate LS problems. For example, in this case I could may as well solve two different LS problems, using $F_1$ and $F_2$ separately. Based on my experience, I think that breaking the problem is faster, but I would like to hear more from someone who has also experienced this problem.
2) Are there in general any differences in the accuracy of the two proposed solutions? Or does the accuracy depend on the characteristics of a specific problem?