## An Analysis of Weighted Least Squares Method and Layered Least Squares Method with the Basis Block Lower Triangular Matrix Form

In this paper, we analyze the limiting behavior of the weighted least squares problem $\min_{x\in\Re^n}\sum_{i=1}^p\|D_i(A_ix-b_i)\|^2$, where each $D_i$ is a positive definite diagonal matrix. We consider the situation where the magnitude of the weights are drastically different block-wisely so that $\max(D_1)\geq\min(D_1) \gg \max(D_2) \geq \min(D_2) \gg \max(D_3) \geq \ldots \gg \max(D_{p-1}) \geq \min(D_{p-1}) \gg \max(D_p)$. … Read more