I'm following an algorithm for computing sparse singular vectors for an SVD decomposition. a part of the algorithm states:
- set initial values $u^{0}$ and $v^{0}$ and set $i=0$
update $u$:
$u^{i+1} \leftarrow Kv^{i}$
$u^{i+1} \leftarrow {u^{i+1} \over \Vert u^{i+1} \Vert}$
$u_{j}^{i+1} \leftarrow (\vert u_{j}^{i+1} \vert - {1 \over 2} \lambda) $....
Where $u$ and $v$ are left and right SVD matrices of singular vectors, and $K$ is a matrix. I'm wondering what the super and subscripts mean in these contexts? I think the $j$ refers to a column, but does $u^{i+1}$ mean raise that vector to that power? Do $u^{0}, v^{0}$ mean set everything to 1 in those vectors?
For the full algorithm:
In the full algorithm you also notice the variables $p $ and $q$, those are the column dimensions of two matrices(A, B, where shape(A) = (n x p), shape(B) = (n x q)) which were used to make up $K$