Algorithm 3.

Intertwined power method.

Input: vector in block, F, with rank RF

Output: improved vector in block, F, with rank RF

(1) Initialization:

(a) compute matrix-vector product: $\left(\mathbf{H}-E_{s}1\right)\mathbf{F}=\mathbf{G}$

(b) construct $\mathbf{B}$ and $\mathbf{P}$ matrices

(2) for $\alpha =1\dots N_{sweep}$:

For $c=1\dots D$: (Loop over coordinates)

(a) downdate: $B_{r^{\prime },r}^{\ne c}\leftarrow B_{r^{\prime },r}∕B_{r^{\prime },r}^c$ for all $r^{\prime }$, r

(b) downdate: $P_{r^{\prime },r}^{\ne c}\leftarrow P_{r^{\prime },r}∕P_{r^{\prime },r}^c$ for all $r^{\prime }$, r

(c) compute $b_r^{\left(i_c,c\right)}$ for all ic, r (Eq. (10))

(d) solve linear system for ${\mathbf{x}}^{\left(i_c,c\right)}$ (Eq. (11));

replace $f_{i_c}^{\left(r,c\right)}\leftarrow x_r^{\left(i_c,c\right)}$ for all ic, r

(e) normalize $s_r^{\mathbf{F}}\leftarrow ∥\mathbf{f}{}^{\left(r,c\right)}∥$; $\mathbf{f}{}^{\left(r,c\right)}\leftarrow \frac{\mathbf{f}{}^{\left(r,c\right)}}{∥\mathbf{f}{}^{\left(r,c\right)}∥}$ for all r;

if c = D: normalize $\mathbf{F}\leftarrow \frac{\mathbf{F}}{∥\mathbf{F}∥}$

(f) update MVP:

For $m=1\dots T$:

For $l=1\dots R_{\psi }$:

$r^{\prime }\leftarrow \left(m-1\right)R_{\psi }+l$

${\mathbf{g}}^{\left(r^{\prime },c\right)}\leftarrow s_l^{\mathbf{F}}{\mathbf{h}}_{m,c}{\mathbf{f}}^{\left(l,c\right)}$

(g) update: $B_{r^{\prime },r}\leftarrow B_{r^{\prime },r}^{\ne c}\cdot B_{r^{\prime },r}^c$ for all $r^{\prime }$, r

(h) update: $P_{r^{\prime },r}\leftarrow P_{r^{\prime },r}^{\ne c}\cdot P_{r^{\prime },r}^c$ for all $r^{\prime }$, r