English

On angles, projections and iterations

Functional Analysis 2020-06-26 v3

Abstract

We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean spaces the convergence of the alternating method is not determined by the principal angles between the subspaces involved. In the second part, we investigate the properties of the Oppenheim angle between two linear projections. We discuss, in particular, the question of existence and uniqueness of "consistency projections" in this context.

Keywords

Cite

@article{arxiv.2004.07540,
  title  = {On angles, projections and iterations},
  author = {Christian Bargetz and Jona Klemenc and Simeon Reich and Natalia Skorokhod},
  journal= {arXiv preprint arXiv:2004.07540},
  year   = {2020}
}

Comments

15 pages; published in "Linear Algebra and Its Applications". This version corrects a number of misprints

R2 v1 2026-06-23T14:53:27.684Z