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We present a Projection onto Convex Sets (POCS) type algorithm for solvingsystems of linear equations. POCS methods have found many applications rangingfrom computer tomography to digital signal and image processing. The Kaczmarzmethod is one of the most popular solvers for overdetermined systems of linearequations due to its speed and simplicity. Here we introduce and analyze anextension of the Kaczmarz method that iteratively projects the estimate onto asolution space given by two randomly selected rows. We show that thisprojection algorithm provides exponential convergence to the solution inexpectation. The convergence rate improves upon that of the standard randomizedKaczmarz method when the system has correlated rows. Experimental resultsconfirm that in this case our method significantly outperforms the randomizedKaczmarz method.

Two-subspace Projection Method for Coherent Overdetermined Systems