Comparing the methods of alternating and simultaneous projections for two subspaces

We study the well-known methods of alternating and simul-taneous projections when applied to two nonorthogonal linear subspaces of a real Euclidean space. Assuming that both of the methods have a common starting point chosen from either one of the subspaces, we show that the method of alternating projections converges significantly faster than the method of simultaneous projections. On the other hand, we provide ex-amples of subspaces and starting points, where the method of simultaneous projections outperforms the method of alternat-ing projections.(c) 2023 Elsevier Inc. All rights reserved.