An algorithmic approach for the analysis of extrapolated iterative schemes applied to least-squares problems

摘要

The 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.