<ref>L.G. Gubin, B.T. Polyak, and E.V. Raik. The method of projections for finding the common point of convex sets. U.S.S.R. Computational Mathematics and Mathematical Physics, 7:1–24, 1967.</ref>
<ref>H.H. Bauschke and J.M. Borwein. On the convergence of von Neumann's alternating projection algorithm for two sets. Set-Valued Analysis, 1:185–212, 1993.</ref>
There are now extensions that consider cases when there are more than one set, or when the sets are not [[convex set|convex]],<ref>{{citeCite journal DOI| last1 = Lewis | first1 = A. S. | last2 = Malick | first2 = J. | doi = 10.1287/moor.1070.0291 | title = Alternating Projections on Manifolds | journal = Mathematics of Operations Research | volume = 33 | pages = 216 | year = 2008 | pmid = | pmc = }}</ref> or that give faster convergence rates. Analysis of POCS and related methods attempt to show that the algorithm converges (and if so, find the [[rate of convergence]]), and whether it converges to the [[Projection (linear algebra)#Orthogonal projections|projection]] of the original point. These questions are largely known for simple cases, but a topic of active research for the extensions. There are also variants of the algorithm, such as [[Dykstra's projection algorithm]]. See the references in the [[#Further_reading|further reading]] section for an overview of the variants, extensions and applications of the POCS method; a good historical background can be found in section III of.<ref name="PLC">P. L. Combettes, "The foundations of set theoretic estimation," Proceedings of the IEEE, vol. 81, no. 2, pp. 182–208, February 1993. [http://www.ann.jussieu.fr/~plc/proc.pdf PDF]</ref>
