# The composition of projections onto closed convex sets in Hilbert space is asymptotically regular

Bauschke, Heinz H. (2001) The composition of projections onto closed convex sets in Hilbert space is asymptotically regular. [Preprint]

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## Abstract

The composition of finitely many projections onto closed convex sets in Hilbert space arises naturally in the area of projection algorithms. We show that this composition is asymptotically regular, thus proving the so-called ``zero displacement conjecture'' from \cite{BBL}. The proof relies on a rich mix of results from monotone operator theory, fixed point theory, convex analysis, and linear algebra.

Item Type: Preprint pubdom FALSE 15-xx Linear and multilinear algebra; matrix theory46-xx Functional analysis > 46Cxx Inner product spaces and their generalizations, Hilbert spaces UNSPECIFIED Users 1 not found. 24 Nov 2003 21 Apr 2010 11:13 https://docserver.carma.newcastle.edu.au/id/eprint/139