Alternating projections between two inconsistent affine subspaces with varying relaxation

TL;DR

This paper investigates the convergence behavior of alternating projections between two inconsistent affine subspaces in a Hilbert space, using a Landweber iteration framework with variable relaxation parameters.

Contribution

It introduces new convergence results for alternating projections with varying relaxation, modeled as a Landweber iteration, in the context of inconsistent affine subspaces.

Findings

Established strong convergence under new conditions.

Linked alternating projections to Landweber iteration with variable steps.

Provided theoretical insights into inconsistent affine subspace projections.

Abstract

In a Hilbert space, we study the strong convergence of alternating projections between two inconsistent affine subspaces with varying relaxation on one side. New convergence results are obtained by seeing the alternating projections as a Landweber iteration with variable steps.