Accelerating the Convergence of the Von Neumann-Halperin Method of Alternating Projections

Orthogonal projections onto the intersection of subspaces are useful in signal processing algorithms including iterative decoding of linear dispersion codes for an unknown MIMO channels and equalization for wireless communication systems. The von Neumann-Halperin method of alternating projections (MAP) is an iterative algorithm for determining the orthogonal projection of a given vector in a Hilbert space onto the intersection of a finite number of given closed subspaces using orthogonal projections onto the given individual subspaces. The main practical drawback of the MAP is that it is often slowly convergent. We propose a method for accelerating the convergence of the MAP and demonstrate that the accelerated algorithm gives significant reduction in complexity and running time when the MAP converges slowly