Recently, Jan, Laura, and Radek submitted a paper proposing new techniques for solving a sequence of linear algebraic systems arising in time-domain component separation. The approach we have proposed combines: 1) two-level preconditioner where the second level is built progressively (“on-the-fly”) using so-called subspace recycling and 2) appropriate adaptation of the initial guess for the subsequent system. In our experiments, this provided an interesting speed-up factor of nearly 7. You are welcome to find more details in the paper on arXiv