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Results tagged with matrix-equations
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user 18786
This question is about equations where the unknown itself is a matrix such as Sylvester or Riccati equations. For systems of linear equations (where the unknown is a vector), use "linear-system".
3
votes
1
answer
118
views
Solving for $X$ in $\sum_{a,b} b a^T b^T X a = Y$
Suppose I have $k$ pairs of $(a,b)$ where $a$ and $b$ are vectors in $\mathbb{R}^d$, $Y$ is $d\times d$ and I need least squares solution for $X$ in the following
$$\sum_{(a,b)}^k b a^T (b^T X a) = Y …
- 2,799
3
votes
1
answer
188
views
Solving underdetermined Lyapunov equation?
I'm solving the following for $X$ with $A,B$ singular positive semidefinite matrices.
$$AX + XA = B$$
Because $A$, $B$ are singular, standard Lyapunov solver fails
However, if I heuristically skip div …
- 2,799
5
votes
1
answer
133
views
Solving $AX+X^TB=C$?
Is there a name/standard algorithm to solve the following equation for $X$?
$AX+X^TB=C$
Matrices $A$,$B$,$C$ are dense, diagonalizable, nearly singular, about $1000\times 1000$ in size. I've looked th …
- 2,799
1
vote
0
answers
27
views
Multiplying by E[xy'] where only some statistics of xy' are known
(cross-posted on crossvalidated)
For random variable $(x,y)$ in $\mathbb{R}^{d}\times \mathbb{R}^{d}$ and vector $v \in \mathbb{R}^d$, I need to perform the following matrix vector multiplication.
$$T …
- 2,799
2
votes
1
answer
54
views
Solving MX=N where M is structured as a Gaussian 4th-moment tensor
I'm looking to solve numerically the following equation for $(d,d)$ variable $X$, in Einstein summation notation
$$M_{ijkl}X_{kl}=N_{ij}$$
Where $M$ is a $(d,d,d,d)$ 4th-moment tensor of random variab …
- 2,799
5
votes
1
answer
246
views
Solving $AXB + X\odot C = D$ matrix equation
Can anyone see a way to solve this equation efficiently?
$$AXB + X\odot C = D$$
I tried a straightforward solution that involved vectorizing $X$ but that turned out too expensive for my application …
- 2,799