# LS solution vs. pre-averaging

by divB
Tags: preaveraging, solution
 P: 81 Hi, I have a system of equations $\mathbf{y} = \mathbf{A}\mathbf{c}$ where the entries in $\mathbf{c}$ are small (say, K=10 elements) and the number equations (i.e., elements in $\mathbf{y}$) is huge (say, N=10000 elements). I want to solve now for $\mathbf{c}$; this can be done using LS with the Pseudo inverse: $$\mathbf{c} = \mathbf{A}^{\dagger} \mathbf{y}$$ However, the vector $\mathbf{y}$ is now heavily corrupted by noise (just assume iid Gaussian). I could calculate the mean over M consecutive elements in $\mathbf{y}$ and rows in $\mathbf{A}$ in order to average over the noise. The system would be collapsed to a smaller system with N/M entries which would be solved via LS. Now I ask the question: Is this better than directly using LS with the full system? I doubt because that's the sense of LS. However, I was not able to "proof" this analytically. Any help? Thanks,