CUR Decomposition

CUR Decomposition

$$
A \simeq C U R \
C = A(:,q) \
R = A(p,:) \
U = C^\dagger A R^\dagger \
p \text{ is a subset of } {1, \dots, m} \
q \text{ is a subset of } {1, \dots, n} \
$$

$$
A \in \mathbb{R}^{m \times n} \
A = VSW^\top \
S \in \mathbb{R}^{k \times k} \
$$

DEIM then is used to find $p$ and $q$ from $V$ and $W$.

$p$