**When:** 9:30 am, Wed, 23rd Oct 2013

**Room:** V205, Mathematics Building

**Access Grid Venue:** Andrew.Danson@newcastle.edu.au

**Speaker:** Laureate Prof Jon Borwein, CARMA, The University of Newcastle

**Title:** *Douglas-Rachford Feasibility Methods For Matrix Completion Problems*

**Abstract:** *Many successful non-convex applications of the Douglas-Rachford method can be viewed as the reconstruction of a matrix, with known properties, from a subset of its entries. In this talk we discuss recent successful applications of the method to a variety of (real) matrix reconstruction problems, both convex and non-convex.
*

This is joint work with Fran Aragón and Matthew Tam.

**Speaker:** Prof Heinz Bauschke, Mathematics and Statistics, UBC Okanagan

**Title:** *The Douglas–Rachford algorithm for two subspaces*

**Abstract:** *I will report on recent joint work (with J.Y. Bello Cruz, H.M. Phan, and X. Wang) on the Douglas–Rachford algorithm for finding a point in the intersection of two subspaces. We prove that the method converges strongly to the projection of the starting point onto the intersection. Moreover, if the sum of the two subspaces is closed, then the convergence is linear with the rate being the cosine of the Friedrichs angle between the subspaces. Our results improve upon existing results in three ways: First, we identify the location of the limit and thus reveal the method as a best approximation algorithm; second, we quantify the rate of convergence, and third, we carry out our analysis in general (possibly infinite-dimensional) Hilbert space. We also provide various examples as well as a comparison with the classical method of alternating projections.*