An algorithmic approach for the analysis of extrapolated iterative schemes applied to least-squares problemsAn algorithmic approach for the analysis of extrapolated iterative schemes applied to least-squares problems Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-161988enThe problem of determining the optimal values of extrapolated iterative schemes, as they apply to the solution of large-scale least-squares problems, is addressed here. Based on algebraic and geometric eigenvalue properties of the Accelerated Gauss—Seidel (AGS), we devise a simple algorithmic procedure, which successfully yields the optimal values of the Extrapolated AGS (EAGS). Comparisons with the optimal SOR scheme reveal that the two optimal schemes strongly compete. Numerical examples are used to demonstrate our results.http://creativecommons.org/licenses/by/4.0/Journal of Computational and Applied Mathematics1-224 209–225 Saridakis Ioannis Σαριδακης Ιωαννης Elsevier Greek mathematics mathematics greek greek mathematics