STIMATING THE M INIMAL B ACKWARD E RROR IN LSQR

Abstract In this paper we propose practical and efficiently-computab le stopping criteria for the iterative solution of large sparse linear least squares (LS) problems. A lthough we focus our discussion on the algorithm LSQR of Paige and Saunders, many ideas discussed here are als o app icable to other conjugate gradients type algorithms. We review why the 2-norm of the projection of the residual vector onto the range of A is a useful measure of convergence, and show how this projection can be e stimated efficiently at every iteration of LSQR. We also give practical and cheaply-computable estimates of th e minimal backward error for the LS problem.

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