Algorithm 1.

Iterative Subspace Screening

Input : A, s, .

Initialization:

1. ${\mathcal{J}}^{\left(0\right)}$ = {. indices of the entries with the largest magnitudes in vector ATs} 2. r(0) = residual $\left(\text{s,}{\mathbf{A}}_{{\mathcal{J}}^{\left(0\right)}}\right)$ 3. f(0) = 0

Iteration : At iterations . = 1, 2, …, go through the following steps:

1. ${\mathcal{J}}^{\left(k\right)}$ = {. indices of the non-zeros entries of f(.−1) and the entries with the largest magnitudes in vector ATr(.−1)} 2. Set f(.) = solve $\left(\text{s,}{\mathbf{A}}_{{\mathcal{J}}^{\left(k\right)}}\right)$ 3. r(.) = residual $\left(\text{s,}{\mathbf{A}}_{{\mathcal{J}}^{\left(k\right)}}\right)$ 4. If ‖r(.)‖>‖r(.−1)‖, quit the iteration.

Output : The solution f = f(.−1).