Iterative methods for least-square problems based on proper splittings

For the linear-squares problems minx ||b−Ax||2, where A is large and sparse, straightforward application of Cholesky or QR factorization will lead to catastrophic fill in factor R. We consider handling such problems by a iterative methods based on proper splittings. We establish the convergence, to the least-square solution y=A†x, for the sequential two-stage iterative method and for the parallel stationary iterative method.