Convergence plots of the first and third step. The LSQR algorithm implementation monitors the convergence status of the solution by computing two parameters, the 2-norm of the residuals vector (||r|| ≡ ||A x − b||), and the 2-norm ||A^T r|| (dashed and solid lines respectively). As mentioned in Sect. 3.2, convergence to the unique least-squares solution is confirmed by the fact that the LSQR estimation of ||A^Tr|| is zero within the machine-precision accuracy.