[__mbm__]

I don't really see a compelling case for this method. The empirical convergence rates are clearly polynomial, while subspace iteration (e.g., Krylov) are "in theory" exponential and in practice pretty good. There is a bit of hand-waving about why Kyrlov methods are not as good (the theory is supposedly not robust to noise), but the techniques for robustifying Krylov-type subspace iterations, such as restarts, are pretty mature.

More than that, the method actually appears to be an iterative "prox" method. These things are very well studied in the convex analysis literature. I wouldn't be surprised if this already appears as a special case of an algorithm in the literature somewhere.