A note on the implementation of the accelerated successive orthogonal projections method for solving large scale linear feasibility problems

In a recent paper we introduced an accelerated version of the Successive Orthogonal Projections method which seems to be useful for solving some classes of large scale linear feasibility problems. The main step of the method involves an orthogonal projection on a linear manifold Bx = b. In this note we consider the very frequent situation where the m X m identity matrix is a submatrix of B. We develop a procedure for computing the projection which only involves “small” matrix factorizations.