All Questions

Given a matrix $L\in \mathbb{R}^{3 \times 3}$, I'm looking for a method to find the closest (in a least squares sense) product of a non-uniform scaling matrix and a rotation matrix: $$ \min_{s\in\...

Consider column vectors $\boldsymbol{z}_i$, $\quad i=1,\dots,n$. Each $\boldsymbol{z}_i$ has $j$ elements and can be expressed as $\boldsymbol{z}_i = \begin{bmatrix} \boldsymbol{x}_i \\ \boldsymbol{y}...

I want to quickly solve the following linear least-squares problem $$\min_{x \in \mathbb{R}^n} \left\| A x - b \right\|_2^2$$ with a special sparse structure where each row in $A$ has only up to $4$ ...

I would like to solve the following optimization problem in $k$-vector $w_i$ $$ \min_{w_i} \quad \left\|P_i - X \mbox{diag} (w_i) Y^T \right\|_F^2 $$ where $P_i$ is a $6 \times 6$ matrix, $X$ and $Y$ ...