2023/06/21 by Simeon Reich, Reich, Simeon, Rafał Zalas +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2306.12219
openalex publication_date 2023/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the well-known methods of alternating and simultaneous 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 examples of subspaces and starting points, where the method of simultaneous projections outperforms the method of alternating projections.