Accelerating the alternating projection algorithm for the case of affine subspaces using supporting hyperplanes

作者：Pang C H Jeffrey^*

来源：Linear Algebra and Its Applications, 2015, 469: 419-439.

DOI：10.1016/j.laa.2014.11.035

• Best approximation problem
• Alternating projections
• Supporting hyperplanes

The von Neumann-Halperin method of alternating projections converges strongly to the projection of a given point onto the intersection of finitely many closed affine subspaces. We propose acceleration schemes making use of two ideas: Firstly, each projection onto an affine subspace identifies a hyperplane of codimension 1 containing the intersection, and secondly, it is easy to project onto a finite intersection of such hyperplanes. We give conditions for which our accelerations converge strongly. Finally, we perform numerical experiments to show that these accelerations perform well for a matrix model updating problem.

• 出版日期2015-3-15