0
votes
1answer
87 views

Bounded domain matrix factorization

Assume we're trying to find $A\in [-1,1]^{n\times d}, B\in [-1,1]^{m\times d}$, from an observed matrix $C\in [-d,d]^{n\times m}$, where $C=AB^T$. The goal is to return $\widehat A, \widehat B$ such ...
4
votes
0answers
60 views

Efficiently factorize a KKT system with block diagonal upper corner

I have a system resulting from a quadratic energy minimization with linear equality constraints enforced with Lagrange multipliers which has the form: \begin{equation} A = \left[\begin{array}{c|c} ...
0
votes
1answer
130 views

“locally” factoring subgroups of Lie groups

I'm not really a math person, and apologize if the question here is too simple. I've ended up with the following type of question for a few Lie groups, but state it for SO(n). I start with a subgroup ...
7
votes
1answer
188 views

Adding a multiple of the Identity to a LU factorized matrix

Suppose a square, dense, symmetric matrix $A$ has been factorized into $L$ and $U$ components by performing a LU decomposition. Now let $B = A+\lambda I$. Is there any way to efficiently compute the ...
6
votes
2answers
4k views

Fast trace of inverse of a square matrix

Which would be the most efficient way (in computational time) to compute tr(inv(H)), where H is a (dense) square matrix? In my particular problem I also have a LU decomposition of H already ...